Subjects -> MATHEMATICS (Total: 1028 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (729 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (26 journals)
    - PROBABILITIES AND MATH STATISTICS (113 journals)

MATHEMATICS (729 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 2)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 1)
Accounting Perspectives     Full-text available via subscription   (Followers: 4)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 13)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 5)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 38)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 2)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 8)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 5)
Advances in Catalysis     Full-text available via subscription   (Followers: 7)
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 20)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 2)
Advances in Fixed Point Theory     Open Access  
Advances in Geosciences (ADGEO)     Open Access   (Followers: 19)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 9)
Advances in Materials Science     Open Access   (Followers: 19)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 18)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Operator Theory     Hybrid Journal  
Advances in Pure Mathematics     Open Access   (Followers: 8)
Advances in Science and Research (ASR)     Open Access   (Followers: 8)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 7)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 5)
Afrika Matematika     Hybrid Journal   (Followers: 2)
Air, Soil & Water Research     Open Access   (Followers: 6)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access  
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 3)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 3)
Algebra and Logic     Hybrid Journal   (Followers: 7)
Algebra Colloquium     Hybrid Journal   (Followers: 1)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 8)
American Journal of Mathematical Analysis     Open Access   (Followers: 1)
American Journal of Mathematical and Management Sciences     Hybrid Journal  
American Journal of Mathematics     Full-text available via subscription   (Followers: 8)
American Journal of Operations Research     Open Access   (Followers: 7)
American Mathematical Monthly     Full-text available via subscription   (Followers: 3)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 12)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 2)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 9)
Anargya : Jurnal Ilmiah Pendidikan Matematika     Open Access  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 3)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – 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: 14)
Annals of Functional Analysis     Hybrid Journal   (Followers: 2)
Annals of Mathematics     Full-text available via subscription   (Followers: 3)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 16)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 4)
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   (Followers: 1)
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access   (Followers: 1)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 3)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 16)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 10)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 2)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 4)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 1)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal  
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 19)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Research Journal of Mathematics     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
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)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 2)
Banach Journal of Mathematical Analysis     Hybrid Journal  
Basin Research     Hybrid Journal   (Followers: 6)
BIBECHANA     Open Access  
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription  
British Journal for the History of Mathematics     Hybrid Journal  
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 17)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 1)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 3)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 2)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 3)
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics     Open Access  
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 2)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Cadernos do IME : Série Matemática     Open Access  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access  
Catalysis in Industry     Hybrid Journal  
CEAS Space Journal     Hybrid Journal   (Followers: 6)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 1)
Chaos, Solitons & Fractals : X     Open Access   (Followers: 1)
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  
Ciencia     Open Access  
CODEE Journal     Open Access  
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 2)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 18)
Commentarii Mathematici Helvetici     Hybrid Journal  
Communications in Advanced Mathematical Sciences     Open Access  
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: 5)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Compositio Mathematica     Full-text available via subscription  
Comptes Rendus : Mathematique     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 3)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 1)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 11)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 9)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 8)
Confluentes Mathematici     Hybrid Journal  
Constructive Mathematical Analysis     Open Access  
Contributions to Discrete Mathematics     Open Access  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal   (Followers: 1)
Cross Section     Full-text available via subscription   (Followers: 1)
Cryptography and Communications     Hybrid Journal   (Followers: 10)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal  
Daya Matematis : Jurnal Inovasi Pendidikan Matematika     Open Access  
Demographic Research     Open Access   (Followers: 14)
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 33)
Desimal : Jurnal Matematika     Open Access  
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Differentsial'nye Uravneniya     Open Access  
Digital Experiences in Mathematics Education     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access   (Followers: 1)
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  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Eco Matemático     Open Access  

        1 2 3 4 | Last

Similar Journals
Journal Cover
COMBINATORICA
Journal Prestige (SJR): 1.764
Citation Impact (citeScore): 1
Number of Followers: 0  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1439-6912 - ISSN (Online) 0209-9683
Published by Springer-Verlag Homepage  [2484 journals]
  • An Analytic Approach to Cardinalities of Sumsets Dávid Matolcsi, Imre Z.
           Ruzsa, George Shakan, Dmitrii Zhelezov

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      Abstract: Let d be a positive integer and U ⊂ ℤd finite. We study $$\beta (U): = \mathop {\inf }\limits_{\mathop {A,B \ne \phi }\limits_{{\rm{finite}}} } {{\left {A + B + U} \right } \over {{{\left A \right }^{1/2}}{{\left B \right }^{1/2}}}},$$ and other related quantities. We employ tensorization, which is not available for the doubling constant, ∣U + U∣/∣U∣. For instance, we show $$\beta (U) = \left U \right ,$$ whenever U is a subset of {0,1}d. Our methods parallel those used for the Prékopa—Leindler inequality, an integral variant of the Brunn—Minkowski inequality.
      PubDate: 2022-01-14
       
  • Algebraic Constructions of Complete m-Arcs Daniele Bartoli, Giacomo
           Micheli

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      Abstract: Let m be a positive integer, q be a prime power, and PG(2,q) be the projective plane over the finite field \({\mathbb{F}_q}\) . Finding complete m-arcs in PG(2,q) of size less than q is a classical problem in finite geometry. In this paper we give a complete answer to this problem when q is relatively large compared with m, explicitly constructing the smallest m-arcs in the literature so far for any m ≥ 8. For any fixed m, our arcs \({{\cal A}_{q,m}}\) satisfy \(\left {{{\cal A}_{q,m}}} \right - q \to - \infty \) as q grows. To produce such m-arcs, we develop a Galois theoretical machinery that allows the transfer of geometric information of points external to the arc, to arithmetic one, which in turn allows to prove the m-completeness of the arc.
      PubDate: 2022-01-14
       
  • Bipartite Turán Problems for Ordered Graphs Abhishek Methuku,
           István Tomon

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      Abstract: A zero-one matrix M contains a zero-one matrix A if one can delete some rows and columns of M, and turn some 1-entries into 0-entries such that the resulting matrix is A. The extremal number of A, denoted by ex(n, A), is the maximum number of 1-entries in an n × n sized matrix M that does not contain A. A matrix A is column-t-partite (or row-t-partite), if it can be cut along the columns (or rows) into t submatrices such that every row (or column) of these submatrices contains at most one 1-entry. We prove that if A is column-t-partite, then \({\rm{ex}}(n,A) < {n^{2 - {1 \over t} + {1 \over {{t^2}}} + o(1)}}\) and if A is both column- and row-t-partite, then \({\rm{ex}}(n,A) < {n^{2 - {1 \over t} + o(1)}}\) . Our proof combines a novel density-increment-type argument with the celebrated dependent random choice method. Results about the extremal numbers of zero-one matrices translate into results about the Turán numbers of bipartite ordered graphs. In particular, a zero-one matrix with at most t 1-entries in each row corresponds to a bipartite ordered graph with maximum degree t in one of its vertex classes. Our results are partially motivated by a well-known result of Füredi (1991) and Alon, Krivelevich, Sudakov (2003) stating that if H is a bipartite graph with maximum degree t in one of the vertex classes, then \({\rm{ex}}(n,H) = O({n^{2 - {1 \over t}}})\) . The aim of the present paper is to establish similar general results about the extremal numbers of ordered graphs.
      PubDate: 2022-01-14
       
  • Probabilistic Refinement of the Asymptotic Spectrum of Graphs

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      Abstract: The asymptotic spectrum of graphs, introduced by Zuiddam (Combinatorica, 2019), is the space of graph parameters that are additive under disjoint union, multiplicative under the strong product, normalized and monotone under homomorphisms between the complements. He used it to obtain a dual characterization of the Shannon capacity of graphs as the minimum of the evaluation function over the asymptotic spectrum and noted that several known upper bounds, including the Lovász number and the fractional Haemers bounds are in fact elements of the asymptotic spectrum (spectral points). We show that every spectral point admits a probabilistic refinement and characterize the functions arising in this way. This reveals that the asymptotic spectrum can be parameterized with a convex set and the evaluation function at every graph is logarithmically convex. One consequence is that for any incomparable pair of spectral points f and g there exists a third one h and a graph G such that h(G) < min{f(G),g(G)}, thus h gives a better upper bound on the Shannon capacity of G. In addition, we show that the (logarithmic) probabilistic refinement of a spectral point on a fixed graph is the entropy function associated with a convex corner.
      PubDate: 2021-12-01
       
  • Equiangular Lines in Low Dimensional Euclidean Spaces

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      Abstract: We show that the maximum cardinality of an equiangular line system in 14 and 16 dimensions is 28 and 40, respectively, thereby solving a longstanding open problem. We also improve the upper bounds on the cardinality of equiangular line systems in 19 and 20 dimensions to 74 and 94, respectively.
      PubDate: 2021-12-01
       
  • (2K + 1)-Connected Tournaments with Large Minimum Out-Degree are K-Linked

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      Abstract: Pokrovskiy conjectured that there is a function f: ℕ → ℕ such that any 2k-strongly-connected tournament with minimum out and in-degree at least f(k) is k-linked. In this paper, we show that any (2k + 1)-strongly-connected tournament with minimum out-degree at least some polynomial in k is k-linked, thus resolving the conjecture up to the additive factor of 1 in the connectivity bound, but without the extra assumption that the minimum in-degree is large. Moreover, we show the condition on high minimum out-degree is necessary by constructing arbitrarily large tournaments that are (2.5k − 1)-strongly-connected tournaments but are not k-linked.
      PubDate: 2021-12-01
       
  • On Gardner’s Conjecture

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      Abstract: Gardner conjectured that if two bounded measurable sets A, B ⊂ ℝn are equidecomposable by a set of isometries Γ generating an amenable group then A and B admit a measurable equidecomposition by all isometries. Cieśla and Sabok asked if there is a measurable equidecomposition using isometries only in the group generated by Γ. We answer this question negatively.
      PubDate: 2021-11-25
       
  • A Subexponential Size Triangulation of ℝPn

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      Abstract: We break the exponential barrier for triangulations of the real projective space, constructing a trianglation of ℝPn with \({e^{\left({{1 \over 2} + o(1)} \right)\sqrt n \log n}}\) vertices.
      PubDate: 2021-11-25
       
  • On the Critical Exponent for k-Primitive Sets

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      Abstract: A set of positive integers is primitive (or 1-primitive) if no member divides another. Erdős proved in 1935 that the weighted sum ∑1/(n log n) for n ranging over a primitive set A is universally bounded over all choices for A. In 1988 he asked if this universal bound is attained by the set of prime numbers. One source of difficulty in this conjecture is that ∑n−λ over a primitive set is maximized by the primes if and only if λ is at least the critical exponent τ1 ≈ 1.14. A set is k-primitive if no member divides any product of up to k other distinct members. One may similarly consider the critical exponent τk for which the primes are maximal among k-primitive sets. In recent work the authors showed that τ2 < 0.8, which directly implies the Erdős conjecture for 2-primitive sets. In this article we study the limiting behavior of the critical exponent, proving that τk tends to zero as k → ∞.
      PubDate: 2021-11-25
       
  • On Bounding the Diameter of a Distance-Regular Graph

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      Abstract: In this note we investigate how to use an initial portion of the intersection array of a distance-regular graph to give an upper bound for the diameter of the graph. We prove three new diameter bounds. Our bounds are tight for the Hamming d-cube, doubled Odd graphs, the Heawood graph, Tutte’s 8-cage and 12-cage, the generalized dodecagons of order (1, 3) and (1, 4), the Biggs-Smith graph, the Pappus graph, the Wells graph, and the dodecahedron.
      PubDate: 2021-11-25
       
  • Kissing Numbers of Regular Graphs

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      Abstract: We prove a sharp upper bound on the number of shortest cycles contained inside any connected graph in terms of its number of vertices, girth, and maximal degree. Equality holds only for Moore graphs, which gives a new characterization of these graphs. In the case of regular graphs, our result improves an inequality of Teo and Koh. We also show that a subsequence of the Ramanujan graphs of Lubotzky-Phillips-Sarnak have super-linear kissing numbers.
      PubDate: 2021-11-25
       
  • Excluding a Ladder

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      Abstract: A ladder is a 2 × k grid graph. When does a graph class \({\cal C}\) exclude some ladder as a minor' We show that this is the case if and only if all graphs G in \({\cal C}\) admit a proper vertex coloring with a bounded number of colors such that for every 2-connected subgraph H of G, there is a color that appears exactly once in H. This type of vertex coloring is a relaxation of the notion of centered coloring, where for every connected subgraph H of G, there must be a color that appears exactly once in H. The minimum number of colors in a centered coloring of G is the treedepth of G, and it is known that classes of graphs with bounded treedepth are exactly those that exclude a fixed path as a subgraph, or equivalently, as a minor. In this sense, the structure of graphs excluding a fixed ladder as a minor resembles the structure of graphs without long paths. Another similarity is as follows: It is an easy observation that every connected graph with two vertex-disjoint paths of length k has a path of length k+1. We show that every 3-connected graph which contains as a minor a union of sufficiently many vertex-disjoint copies of a 2×k grid has a 2×(k+1) grid minor. Our structural results have applications to poset dimension. We show that posets whose cover graphs exclude a fixed ladder as a minor have bounded dimension. This is a new step towards the goal of understanding which graphs are unavoidable as minors in cover graphs of posets with large dimension.
      PubDate: 2021-11-25
       
  • On the Ramsey-Turán Density of Triangles

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      Abstract: One of the oldest results in modern graph theory, due to Mantel, asserts that every triangle-free graph on n vertices has at most ⌊n2/4⌋ edges. About half a century later Andrásfai studied dense triangle-free graphs and proved that the largest triangle-free graphs on n vertices without independent sets of size αn, where 2/5 ≤ α < 1/2, are blow-ups of the pentagon. More than 50 further years have elapsed since Andrásfai’s work. In this article we make the next step towards understanding the structure of dense triangle-free graphs without large independent sets. Notably, we determine the maximum size of triangle-free graphs G on n vertices with α(G) ≥ 3n/8 and state a conjecture on the structure of the densest triangle-free graphs G with α(G) > n/3. We remark that the case α(G) α n/3 behaves differently, but due to the work of Brandt this situation is fairly well understood.
      PubDate: 2021-11-24
       
  • Bounded VC-Dimension Implies the Schur-Erdős Conjecture

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      Abstract: In 1916, Schur introduced the Ramsey number r(3; m), which is the minimum integer n > 1 such that for any m-coloring of the edges of the complete graph Kn, there is a monochromatic copy of K3. He showed that r(3; m) ≤ O(m!), and a simple construction demonstrates that r(3; m) ≥ 2Ω(m). An old conjecture of Erdős states that r(3; m) = 2Θ(m). In this note, we prove the conjecture for m-colorings with bounded VC-dimension, that is, for m-colorings with the property that the set system induced by the neighborhoods of the vertices with respect to each color class has bounded VC-dimension.
      PubDate: 2021-11-20
       
  • Substitutive Systems and a Finitary Version of Cobham’s Theorem

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      Abstract: We study substitutive systems generated by nonprimitive substitutions and show that transitive subsystems of substitutive systems are substitutive. As an application we obtain a complete characterisation of the sets of words that can appear as common factors of two automatic sequences defined over multiplicatively independent bases. This generalises the famous theorem of Cobham.
      PubDate: 2021-11-20
       
  • The Ramsey Properties for Grassmannians Over ℝ, ℂ

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      Abstract: In this note we study and obtain factorization theorems for colorings of matrices and Grassmannians over ℝ and ℂ, which can be considered metric versions of the Dual Ramsey Theorem for Boolean matrices and of the Graham-Leeb-Rothschild Theorem for Grassmannians over a finite field.
      PubDate: 2021-11-20
       
  • On the Directions Determined by a Cartesian Product in an Affine Galois
           Plane

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      Abstract: We prove that the number of directions contained in a set of the form A × B ⊂ AG(2,p), where p is prime, is at least A B − min{ A , B } + 2. Here A and B are subsets of GF(p) each with at least two elements and A B <p. This bound is tight for an infinite class of examples. Our main tool is the use of the Rédei polynomial with Szőnyi’s extension. As an application of our main result, we obtain an upper bound on the clique number of a Paley graph, matching the current best bound obtained recently by Hanson and Petridis.
      PubDate: 2021-11-20
       
  • Convergence and Limits of Finite Trees

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      Abstract: Motivated by the work of Lovász and Szegedy on the convergence and limits of dense graph sequences [10], we investigate the convergence and limits of finite trees with respect to sampling in normalized distance. We introduce dendrons (a notion based on separable real trees) and show that the sampling limits of finite trees are exactly the dendrons. We also prove that the limit dendron is unique.
      PubDate: 2021-11-15
       
  • Lower Bounds on the Chromatic Number of Random Graphs

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      Abstract: We prove that a formula predicted on the basis of non-rigorous physics arguments [Zdeborová and Krzakala: Phys. Rev. E (2007)] provides a lower bound on the chromatic number of sparse random graphs. The proof is based on the interpolation method from mathematical physics. In the case of random regular graphs the lower bound can be expressed algebraically, while in the case of the binomial random we obtain a variational formula. As an application we calculate improved explicit lower bounds on the chromatic number of random graphs for small (average) degrees. Additionally, we show how asymptotic formulas for large degrees that were previously obtained by lengthy and complicated combinatorial arguments can be re-derived easily from these new results.
      PubDate: 2021-10-26
       
  • A Cap Covering Theorem

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      Abstract: A cap of spherical radius α on a unit d-sphere S is the set of points within spherical distance α from a given point on the sphere. Let \({\cal F}\) be a finite set of caps lying on S. We prove that if no hyperplane through the center of S divides \({\cal F}\) into two non-empty subsets without intersecting any cap in \({\cal F}\) , then there is a cap of radius equal to the sum of radii of all caps in \({\cal F}\) covering all caps of \({\cal F}\) provided that the sum of radii is less than π/2. This is the spherical analog of the so-called Circle Covering Theorem by Goodman and Goodman and the strengthening of Fejes Tóth’s zone conjecture proved by Jiang and the author.
      PubDate: 2021-10-01
       
 
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