Results 21 to 30 of about 14,274 (218)
New results in extremal combinatorics
, 2021 Extremal problems, in general, ask for the optimal size of certain finite objects when some restrictions are imposed. In extremal combinatorics, a major field in combinatorics, one studies how global properties guarantee the existence of local substructures, or equivalently, how avoiding local substructures poses a constraint on global quantities.
Ching Wong
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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.
Fedor V. Fomin, Yngve Villanger
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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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Extremal problems and the combinatorics of sumsets [PDF]
, 2023 18 pages.
Melvyn B. Nathanson
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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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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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Extremal Combinatorics and Universal Algorithms
, 2018 In this dissertation we solve several combinatorial problems in different areas of mathematics: automata theory, combinatorics of partially ordered sets and extremal combinatorics. Firstly, we focus on some new automata that do not seem to have occurred much in the literature, that of solvability of mazes.
Stefan David
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Fully Computer-Assisted Proofs in Extremal Combinatorics
Proceedings of the AAAI Conference on Artificial Intelligence, 2023 We present a fully computer-assisted proof system for solving a particular family of problems in Extremal Combinatorics. Existing techniques using Flag Algebras have proven powerful in the past, but have so far lacked a computational counterpart to derive matching constructive bounds.
Olaf Parczyk +3 more
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Problems in Coding Theory and Extremal Combinatorics
, 2020 This dissertation consists of ?five papers whose subjects are mostly disjoint. Below are their abstracts and citation information.On a fractional version of Haemers' bound. In this note, we present a fractional version of Haemers' bound on the Shannon capacity of a graph, which is originally due to Blasiak.
Christopher Cox
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Coloring and extremal problems in combinatorics
, 2010 Coloring problems concern partitions of structures. The classic problem of partitioning the set of integers into a finite number of pieces so that no one piece has an arithmetic progression of a fixed length was solved in 1927. Van der Waerden's Theorem shows that it is impossible to do so.
Jacob Manske
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