Results 1 to 10 of about 284 (146)
PPP-Completeness and Extremal Combinatorics [PDF]
14thInnovationsinTheoreticalComputerScienceConference(ITCS2023), 2023 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 ...
Romain Bourneuf +4 more
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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.
Timothy F. N. Chan
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Problems and results in Extremal Combinatorics – III [PDF]
Discrete Mathematics, 2016 Extremal Combinatorics is among the most active topics in Discrete Mathematics, dealing with problems that are often motivated by questions in other areas, including Theoretical Computer Science and Information Theory. This paper contains a collection of problems and results in the area, including solutions or partial solutions to open problems ...
Noga Alon
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Graphical designs and extremal combinatorics
Linear Algebra and its Applications, 2020 A graphical design is a proper subset of vertices of a graph on which many eigenfunctions of the Laplacian operator have mean value zero. In this paper, we show that extremal independent sets make extremal graphical designs, that is, a design on which the maximum possible number of eigenfunctions have mean value zero.
Konstantin Golubev
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Extremal Combinatorics, Iterated Pigeonhole Arguments and Generalizations of PPP [PDF]
, 2022 We study the complexity of computational problems arising from existence theorems in extremal combinatorics. For some of these problems, a solution is guaranteed to exist based on an iterated application of the Pigeonhole Principle. This results in the definition of a new complexity class within TFNP, which we call PLC (for "polynomial long choice ...
Amol Pasarkar +2 more
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Two problems in extremal combinatorics
, 2021 In this thesis, we focus on two problems in extremal graph theory. Extremal graph theory consists of all problems related to optimizing parameters defined on graphs. The concept of ``editing'' appears in many key results and techniques in extremal graph theory, either as a means to account for error in structural results, or as a quantity to minimize ...
Alex Neal Riasanovsky
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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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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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Sumsets, Zero-Sums and Extremal Combinatorics
, 2006 This thesis develops and applies a method of tackling zero-sum additive questions, especially those related to the Erdos-Ginzburg-Ziv Theorem (EGZ), through the use of partitioning sequences into sets, i.e., set partitions. Much of the research can alternatively be found in the literature spread across nine separate articles, but is here collected into
David J. Grynkiewicz
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Extremal problems and the combinatorics of sumsets [PDF]
, 2023 18 pages.
Melvyn B. Nathanson
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