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MATHEMATICS (706 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 27)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 6)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 18)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 12)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 2)
Advances in Materials Sciences     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 3)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 5)
Advances in Science and Research (ASR)     Open Access   (Followers: 4)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 11)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 5)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 8)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 11)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 11)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 2)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 20)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 11)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 4)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 8)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 9)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 10)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 29)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 4)

        1 2 3 4 | Last

  [SJR: 1.296]   [H-I: 38]   [0 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1439-6912 - ISSN (Online) 0209-9683
   Published by Springer-Verlag Homepage  [2351 journals]
  • Asymptotic Metric Behavior of Random Cayley Graphs of Finite Abelian
    • Authors: Uri Shapira; Reut Zuck
      Abstract: Using methods of Marklof and Strömbergsson we establish several limit laws for metric parameters of random Cayley graphs of finite abelian groups with respect to a randomly chosen set of generators of a fixed size. Doing so we settle a conjecture of Amir and Gurel- Gurevich.
      PubDate: 2018-02-07
      DOI: 10.1007/s00493-017-3672-2
  • On the Size of K -Cross-Free Families
    • Authors: Andrey Kupavskii; János Pach; István Tomon
      Abstract: Two subsets A,B of an n-element ground set X are said to be crossing, if none of the four sets A∩B, A\B, B\A and X\(A∪B) are empty. It was conjectured by Karzanov and Lomonosov forty years ago that if a family F of subsets of X does not contain k pairwise crossing elements, then F =O(kn). For k=2 and 3, the conjecture is true, but for larger values of k the best known upper bound, due to Lomonosov, is F =O(knlogn). In this paper, we improve this bound for large n by showing that F =O k (nlog*n) holds, where log* denotes the iterated logarithm function.
      PubDate: 2018-02-07
      DOI: 10.1007/s00493-017-3792-8
  • Ramsey Graphs Induce Subgraphs of Many Different Sizes
    • Authors: Bhargav Narayanan; Julian Sahasrabudhe; István Tomon
      Abstract: A graph on n vertices is said to be C-Ramsey if every clique or independent set of the graph has size at most C logn. The only known constructions of Ramsey graphs are probabilistic in nature, and it is generally believed that such graphs possess many of the same properties as dense random graphs. Here, we demonstrate one such property: for any fixed C > 0, every C-Ramsey graph on n vertices induces subgraphs of at least n2-o(1) distinct sizes. This near-optimal result is closely related to two unresolved conjectures, the first due to Erdős and McKay and the second due to Erdős, Faudree and Sós, both from 1992.
      PubDate: 2018-02-07
      DOI: 10.1007/s00493-017-3755-0
  • Associahedra Via Spines
    • Authors: Carsten Lange; Vincent Pilaud
      Abstract: An associahedron is a polytope whose vertices correspond to triangulations of a convex polygon and whose edges correspond to flips between them. Using labeled polygons, C. Hohlweg and C. Lange constructed various realizations of the associahedron with relevant properties related to the symmetric group and the permutahedron. We introduce the spine of a triangulation as its dual tree together with a labeling and an orientation. This notion extends the classical understanding of the associahedron via binary trees, introduces a new perspective on C. Hohlweg and C. Lange’s construction closer to J.-L. Loday’s original approach, and sheds light upon the combinatorial and geometric properties of the resulting realizations of the associahedron. It also leads to noteworthy proofs which shorten and simplify previous approaches.
      PubDate: 2018-02-07
      DOI: 10.1007/s00493-015-3248-y
  • A Ramsey Statement for Infinite Groups
    • Authors: Péter Komjáth
      Abstract: If κ is a cardinal, n < ω, then there exists an Abelian group G such that if F : G→κ, then there exist distinct elements ai,α ∈ G (1≤i≤n, α<κ), and a color τ < κ such that if 1≤i0<⋯<i r ≤n, α1,...,α r <κ, then \(F\left( {{a_{{i_1},{\alpha _1}}} + \cdots + {a_{{i_r},{\alpha _r}}}} \right) = \tau \) .
      PubDate: 2018-02-03
      DOI: 10.1007/s00493-016-3706-1
  • Distance-Preserving Subgraphs of Johnson Graphs
    • Authors: Victor Chepoi
      Pages: 1039 - 1055
      Abstract: We give a characterization of distance-preserving subgraphs of Johnson graphs, i.e., of graphs which are isometrically embeddable into Johnson graphs (the Johnson graph J(m,∧) has the subsets of cardinality m of a set ∧ as the vertex-set and two such sets A,B are adjacent iff AΔB =2). Our characterization is similar to the characterization of D. Ž. Djoković [11] of distance-preserving subgraphs of hypercubes and provides an explicit description of the wallspace (split system) defining the embedding.
      PubDate: 2017-12-01
      DOI: 10.1007/s00493-016-3421-y
      Issue No: Vol. 37, No. 6 (2017)
  • Induced Subgraphs of Graphs with Large Chromatic Number. III. Long Holes
    • Authors: Maria Chudnovsky; Alex Scott; Paul Seymour
      Pages: 1057 - 1072
      Abstract: We prove a 1985 conjecture of Gyárfás that for all k, ℓ, every graph with sufficiently large chromatic number contains either a clique of cardinality more than k or an induced cycle of length more than ℓ.
      PubDate: 2017-12-01
      DOI: 10.1007/s00493-016-3467-x
      Issue No: Vol. 37, No. 6 (2017)
  • Integer 4-Flows and Cycle Covers
    • Authors: Genghua Fan
      Pages: 1097 - 1112
      Abstract: Let G be a bridgeless graph and denote by cc(G) the shortest length of a cycle cover of G. Let V2(G) be the set of vertices of degree 2 in G. It is known that if cc(G)≤1.4 E(G) for every bridgeless graph G with V2(G) ≤ \(\frac{1}{10}\) E(G) , then the Cycle Double Cover Conjecture is true. The best known result cc(G)≤ \(\frac{5}{3}\) E(G) (≈1.6667 E(G) ) was established over 30 years ago. Recently, it was proved that cc(G) ≤ \(\frac{44}{27}\) E(G) (≈ 1.6296 E(G) ) for loopless graphs with minimum degree at least 3. In this paper, we obtain results on integer 4-flows, which are used to find bounds for cc(G). We prove that if G has minimum degree at least 3 (loops being allowed), then cc(G)<1.6258 E(G) . As a corollary, adding loops to vertices of degree 2, we obtain that cc(G)<1.6466 E(G) for every bridgeless graph G with V2(G) ≤ \(\frac{1}{30}\) E(G) .
      PubDate: 2017-12-01
      DOI: 10.1007/s00493-016-3379-9
      Issue No: Vol. 37, No. 6 (2017)
  • On the Number of Edge-Disjoint Triangles in K 4 -Free Graphs
    • Authors: Ervin Győri; Balázs Keszegh
      Pages: 1113 - 1124
      Abstract: We prove the quarter of a century old conjecture that every K4-free graph with n vertices and [n2/4]+m edges contains m pairwise edge-disjoint triangles.
      PubDate: 2017-12-01
      DOI: 10.1007/s00493-016-3500-0
      Issue No: Vol. 37, No. 6 (2017)
  • Decomposing a Graph into Forests: The Nine Dragon Tree Conjecture is True
    • Authors: Hongbi Jiang; Daqing Yang
      Pages: 1125 - 1137
      Abstract: The fractional arboricity of a graph G, denoted by Γf (G), is defined as $${\Gamma _f}\left( G \right) = {\max _{H \subseteq G,v\left( H \right) > 1}}\frac{{e\left( H \right)}}{{v\left( H \right) - 1}}$$ . The celebrated Nash-Williams’ Theorem states that a graph G can be partitioned into at most k forests if and only if Γf (G)≤k. The Nine Dragon Tree (NDT) Conjecture [posed by Montassier, Ossona de Mendez, Raspaud, and Zhu, in “Decomposing a graph into forests”, J. Combin. Theory Ser. B 102 (2012) 38-52] asserts that if $${\Gamma _f}\left( G \right) \leqslant k + \frac{d}{{k + d + 1}}$$ , then G decomposes into k+1 forests with one having maximum degree at most d. In this paper, we prove the Nine Dragon Tree (NDT) Conjecture.
      PubDate: 2017-12-01
      DOI: 10.1007/s00493-016-3390-1
      Issue No: Vol. 37, No. 6 (2017)
  • On-Line Approach to Off-Line Coloring Problems on Graphs with Geometric
    • Authors: Tomasz Krawczyk; Bartosz Walczak
      Pages: 1139 - 1179
      Abstract: The main goal of this paper is to formalize and explore a connection between chromatic properties of graphs with geometric representations and competitive analysis of on-line algorithms, which became apparent after the recent construction of triangle-free geometric intersection graphs with arbitrarily large chromatic number due to Pawlik et al. We show that on-line graph coloring problems give rise to classes of game graphs with a natural geometric interpretation. We use this concept to estimate the chromatic number of graphs with geometric representations by finding, for appropriate simpler graphs, on-line coloring algorithms using few colors or proving that no such algorithms exist. We derive upper and lower bounds on the maximum chromatic number that rectangle overlap graphs, subtree overlap graphs, and interval filament graphs (all of which generalize interval overlap graphs) can have when their clique number is bounded. The bounds are absolute for interval filament graphs and asymptotic of the form (log logn)f(ω) for rectangle and subtree overlap graphs, where f(ω) is a polynomial function of the clique number and n is the number of vertices. In particular, we provide the first construction of geometric intersection graphs with bounded clique number and with chromatic number asymptotically greater than log logn. We also introduce a concept of K k -free colorings and show that for some geometric representations, K3-free chromatic number can be bounded in terms of clique number although the ordinary (K2-free) chromatic number cannot. Such a result for segment intersection graphs would imply a well-known conjecture that k-quasi-planar geometric graphs have linearly many edges.
      PubDate: 2017-12-01
      DOI: 10.1007/s00493-016-3414-x
      Issue No: Vol. 37, No. 6 (2017)
  • Proof of Schur’s Conjecture in ℝ D
    • Authors: Andrey B. Kupavskii; Alexandr Polyanskii
      Pages: 1181 - 1205
      Abstract: In this paper we prove Schur’s conjecture in ℝ d , which states that any diameter graph G in the Euclidean space ℝ d on n vertices may have at most n cliques of size d. We obtain an analogous statement for diameter graphs with unit edge length on a sphere S r d of radius \(r>1/\sqrt{2}\) . The proof rests on the following statement, conjectured by F. Morić and J. Pach: given two unit regular simplices Δ1, Δ2 on d vertices in ℝ d , either they share d-2 vertices, or there are vertices v1∈Δ1, v2∈Δ2 such that ‖v1-v2‖>1. The same holds for unit simplices on a d-dimensional sphere of radius greater than \(1/\sqrt{2}\) .
      PubDate: 2017-12-01
      DOI: 10.1007/s00493-016-3340-y
      Issue No: Vol. 37, No. 6 (2017)
  • Bipartite Kneser Graphs are Hamiltonian
    • Authors: Torsten Mütze; Pascal Su
      Pages: 1207 - 1219
      Abstract: For integers k ≥1 and n≥2k+1 the Kneser graph K(n;k) has as vertices all k-element subsets of [n]:={1;2;:::;n} and an edge between any two vertices (=sets) that are disjoint. The bipartite Kneser graph H(n,k) has as vertices all k-element and (n—k)-element subsets of [n] and an edge between any two vertices where one is a subset of the other. It has long been conjectured that all Kneser graphs and bipartite Kneser graphs except the Petersen graph K(5, 2) have a Hamilton cycle. The main contribution of this paper is proving this conjecture for bipartite Kneser graphs H(n,k). We also establish the existence of cycles that visit almost all vertices in Kneser graphs K(n,k) when n=2k+o(k), generalizing and improving upon previous results on this problem.
      PubDate: 2017-12-01
      DOI: 10.1007/s00493-016-3434-6
      Issue No: Vol. 37, No. 6 (2017)
  • The Number of Unit-Area Triangles in the Plane: Theme and Variation
    • Authors: Orit E. Raz; Micha Sharir
      Pages: 1221 - 1240
      Abstract: We show that the number of unit-area triangles determined by a set S of n points in the plane is O(n20/9), improving the earlier bound O(n9/4) of Apfelbaum and Sharir [2]. We also show, using a somewhat subtle construction, that if S consists of points on three lines, the number of unit-area triangles that S spans can be Ω(n2), for any triple of lines (it is always O(n2) in this case).
      PubDate: 2017-12-01
      DOI: 10.1007/s00493-016-3440-8
      Issue No: Vol. 37, No. 6 (2017)
  • Strong inapproximability results on balanced rainbow-colorable hypergraphs
    • Authors: Venkatesan Guruswami; Euiwoong Lee
      Abstract: Consider a K-uniform hypergraph H = (V, E). A coloring c: V → {1, 2, …, k} with k colors is rainbow if every hyperedge e contains at least one vertex from each color, and is called perfectly balanced when each color appears the same number of times. A simple polynomial-time algorithmnds a 2-coloring if H admits a perfectly balanced rainbow k-coloring. For a hypergraph that admits an almost balanced rainbow coloring, we prove that it is NP-hard to find an independent set of size ϵ, for any ϵ > 0. Consequently, we cannot weakly color (avoiding monochromatic hyperedges) it with O(1) colors. With k=2, it implies strong hardness for discrepancy minimization of systems of bounded set-size. One of our main technical tools is based on reverse hypercontractivity. Roughly, it says the noise operator increases q-norm of a function when q < 1, which is enough for some special cases of our results. To prove the full results, we generalize the reverse hypercontractivity to more general operators, which might be of independent interest. Together with the generalized reverse hypercontractivity and recent developments in inapproximability based on invariance principles for correlated spaces, we give a recipe for converting a promising test distribution and a suitable choice of an outer PCP to hardness of nding an independent set in the presence of highly-structured colorings. We use this recipe to prove additional results almost in a black-box manner, including: (1) the rst analytic proof of (K − 1 − ϵ)-hardness of K-Hypergraph Vertex Cover with more structure in completeness, and (2) hardness of (2Q+1)-SAT when the input clause is promised to have an assignment where every clause has at least Q true literals.
      PubDate: 2017-12-14
      DOI: 10.1007/s00493-016-3383-0
  • Extending factorizations of complete uniform hypergraphs
    • Authors: M. A. Bahmanian; Mike Newman
      Abstract: We consider when a given r-factorization of the complete uniform hypergraph on m vertices K m h can be extended to an s-factorization of K n h . The case of r = s = 1 was first posed by Cameron in terms of parallelisms, and solved by Häggkvist and Hellgren. We extend these results, which themselves can be seen as extensions of Baranyai's Theorem. For r=s, we show that the “obvious” necessary conditions, together with the condition that gcd(m,n,h)=gcd(n,h) are sufficient. In particular this gives necessary and sufficient conditions for the case where r=s and h is prime. For r<s we show that the obvious necessary conditions, augmented by gcd(m,n,h)=gcd(n,h), n≥2m, and \(1 \leqslant \frac{s}{r} \leqslant \frac{m}{k}\left[ {1 - \left( {\begin{array}{*{20}{c}} {m - k} \\ h \end{array}} \right)/\left( {\begin{array}{*{20}{c}} m \\ h \end{array}} \right)} \right]\) are sufficient, where k=gcd(m,n,h). We conclude with a discussion of further necessary conditions and some open problems.
      PubDate: 2017-12-09
      DOI: 10.1007/s00493-017-3396-3
  • Finding perfect matchings in bipartite hypergraphs
    • Authors: Chidambaram Annamalai
      Abstract: Haxell’s condition [14] is a natural hypergraph analog of Hall’s condition, which is a wellknown necessary and sufficient condition for a bipartite graph to admit a perfect matching. That is, when Haxell’s condition holds it forces the existence of a perfect matching in the bipartite hypergraph. Unlike in graphs, however, there is no known polynomial time algorithm to find the hypergraph perfect matching that is guaranteed to exist when Haxell’s condition is satisfied. We prove the existence of an efficient algorithm to find perfect matchings in bipartite hypergraphs whenever a stronger version of Haxell’s condition holds. Our algorithm can be seen as a generalization of the classical Hungarian algorithm for finding perfect matchings in bipartite graphs. The techniques we use to achieve this result could be of use more generally in other combinatorial problems on hypergraphs where disjointness structure is crucial, e.g., Set Packing.
      PubDate: 2017-12-09
      DOI: 10.1007/s00493-017-3567-2
  • Multiplicative bases and an Erdős problem
    • Authors: Péter Pál Pach; Csaba Sándor
      Abstract: In this paper we investigate how small the density of a multiplicative basis of order h can be in {1,2,...,n} and in ℤ+. Furthermore, a related problem of Erdős is also studied: How dense can a set of integers be, if none of them divides the product of h others'
      PubDate: 2017-12-09
      DOI: 10.1007/s00493-016-3588-2
  • On the linear span of lattice points in a parallelepiped
    • Authors: Marcel Celaya
      Abstract: Let Λ⊂R n be a lattice which contains the integer lattice Z n . We characterize the space of linear functions R n →R which vanish on the lattice points of Λ lying in the half-open unit cube [0, 1) n . We also find an explicit formula for the dimension of the linear span of Λ∩[0,1) n . The results in this paper generalize and are based on the Terminal Lemma of Reid, which is in turn based upon earlier work of Morrison and Stevens on the classification of four dimensional isolated Gorenstein terminal cyclic quotient singularities.
      PubDate: 2017-12-09
      DOI: 10.1007/s00493-017-3562-7
  • Black-box identity testing of depth-4 multilinear circuits
    • Authors: Shubhangi Saraf; Ilya Volkovich
      Abstract: We study the problem of identity testing for multilinear ΣΠΣΠ(k) circuits, i.e., multilinear depth-4 circuits with fan-in k at the top + gate. We give the first polynomial-time deterministic identity testing algorithm for such circuits when k=O(1). Our results also hold in the black-box setting. The running time of our algorithm is \({\left( {ns} \right)^{{\text{O}}\left( {{k^3}} \right)}}\) , where n is the number of variables, s is the size of the circuit and k is the fan-in of the top gate. The importance of this model arises from [11], where it was shown that derandomizing black-box polynomial identity testing for general depth-4 circuits implies a derandomization of polynomial identity testing (PIT) for general arithmetic circuits. Prior to our work, the best PIT algorithm for multilinear ΣΠΣΠ(k) circuits [31] ran in quasi-polynomial-time, with the running time being \({n^{{\rm O}\left( {{k^6}\log \left( k \right){{\log }^2}s} \right)}}\) . We obtain our results by showing a strong structural result for multilinear ΣΠΣΠ(k) circuits that compute the zero polynomial. We show that under some mild technical conditions, any gate of such a circuit must compute a sparse polynomial. We then show how to combine the structure theorem with a result by Klivans and Spielman [33], on the identity testing for sparse polynomials, to yield the full result.
      PubDate: 2017-12-09
      DOI: 10.1007/s00493-016-3460-4
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