Results 1 to 10 of about 87 (85)
Probabilistic models for the analysis of inverse extremal problems in combinatorics [PDF]
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2022 In an inverse extremal problem for a combinatorial scheme with a given value of the objective function of the form of a certain extreme value of its characteristic, a probabilistic model is developed that ensures that this value is obtained in its ...
Nataliya Yu. Enatskaya
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Exponential multivalued forbidden configurations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 The forbidden number $\mathrm{forb}(m,F)$, which denotes the maximum number of unique columns in an $m$-rowed $(0,1)$-matrix with no submatrix that is a row and column permutation of $F$, has been widely studied in extremal set theory.
Travis Dillon, Attila Sali
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PPP-Completeness and Extremal Combinatorics
14thInnovationsinTheoreticalComputerScienceConference(ITCS2023), 2022 Many classical theorems in combinatorics establish the emergence of substructures within sufficiently large collections of objects. Well-known examples are Ramsey's theorem on monochromatic subgraphs and the Erdős-Rado sunflower lemma. Implicit versions of the corresponding total search problems are known to be PWPP-hard; here "implici" means that the ...
Bourneuf, Romain +4 more
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Ramsey numbers of cycles versus general graphs
Forum of Mathematics, Sigma, 2023 The Ramsey number $R(F,H)$ is the minimum number N such that any N-vertex graph either contains a copy of F or its complement contains H. Burr in 1981 proved a pleasingly general result that, for any graph H, provided n is sufficiently large, a ...
John Haslegrave +3 more
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Treewidth computation and extremal combinatorics [PDF]
Combinatorica, 2008 For a given graph G and integers b,f >= 0, let S be a subset of vertices of G of size b+1 such that the subgraph of G induced by S is connected and S can be separated from other vertices of G by removing f vertices. We prove that every graph on n vertices contains at most n\binom{b+f}{b} such vertex subsets.
Fomin, Fedor V., Villanger, Yngve
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A path forward: Tropicalization in extremal combinatorics
Advances in Mathematics, 2022 Many important problems in extremal combinatorics can be be stated as proving a pure binomial inequality in graph homomorphism numbers, i.e., proving that hom$(H_1,G)^{a_1}\cdots$hom$(H_k,G)^{a_k}\geq$hom$(H_{k+1},G)^{a_{k+1}}\cdots$hom$(H_m,G)^{a_m}$ holds for some fixed graphs $H_1,\dots,H_m$ and all graphs $G$.
Blekherman, Grigoriy, Raymond, Annie
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Information Inequalities via Submodularity and a Problem in Extremal Graph Theory
Entropy, 2022 The present paper offers, in its first part, a unified approach for the derivation of families of inequalities for set functions which satisfy sub/supermodularity properties.
Igal Sason
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Substructure Densities in Extremal Combinatorics [PDF]
, 2021 One of the primary goals of combinatorial mathematics is to understand how an object's properties are influenced by the presence or multiplicity of a given substructure. Over time, it has become popular to highlight the asymptotic behaviour of objects by expressing results in terms of the density of substructures.
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Chromatic Turán problems and a new upper bound for the Turán density of $\mathcal{K}_4^-$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We consider a new type of extremal hypergraph problem: given an $r$-graph $\mathcal{F}$ and an integer $k≥2$ determine the maximum number of edges in an $\mathcal{F}$-free, $k$-colourable $r$-graph on $n$ vertices.
John Talbot
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On the quaternion projective space
Journal of Taibah University for Science, 2020 Apart from being a vital and exciting field in mathematics with interesting results, projective spaces have various applications in design theory, coding theory, physics, combinatorics, number theory and extremal combinatorial problems. In this paper, we
Y. Omar +4 more
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