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Graphical Designs and Extremal Combinatorics [PDF]
Konstantin Golubev,Graphical designs and extremal combinatorics,
Linear Algebra and its Applications, Volume 604, 1 November 2020, Pages
490-506, 2019 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
arxiv +9 more sources
Refuting conjectures in extremal combinatorics via linear programming [PDF]
arXiv, 2019 We apply simple linear programming methods and an LP solver to refute a number of open conjectures in extremal combinatorics.
Adam Zsolt Wagner
arxiv +10 more sources
A path forward: Tropicalization in extremal combinatorics [PDF]
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 $G$.
Grigoriy Blekherman, Annie Raymond
semanticscholar +5 more sources
PPP-Completeness and Extremal Combinatorics [PDF]
Electron. Colloquium Comput. Complex., 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 Erd\H{o}s-Rado sunflower lemma.
Romain Bourneuf +4 more
semanticscholar +6 more sources
High dimensional Hoffman bound and applications in extremal combinatorics [PDF]
Algebraic Combinatorics, 2022 One powerful method for upper-bounding the largest independent set in a graph is the Hoffman bound, which gives an upper bound on the largest independent set of a graph in terms of its eigenvalues. It is easily seen that the Hoffman bound is sharp on the
Yuval Filmus +2 more
semanticscholar +7 more sources
Extremal combinatorics, iterated pigeonhole arguments, and generalizations of PPP [PDF]
Information Technology Convergence and Services, 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.
Amol Pasarkar +2 more
semanticscholar +6 more sources
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
semanticscholar +5 more sources
Reaction systems and extremal combinatorics properties
Theoretical Computer Science, 2015 International ...
Alberto Dennunzio +2 more
semanticscholar +8 more sources
Universal limit theorems in graph coloring problems with connections to extremal combinatorics [PDF]
Annals of Applied Probability, 2017 This paper proves limit theorems for the number of monochromatic edges in uniform random colorings of general random graphs. These can be seen as generalizations of the birthday problem (what is the chance that there are two friends with the same birthday?).
Bhaswar B. Bhattacharya +2 more
exaly +8 more sources
Information Inequalities via Submodularity and a Problem in Extremal Graph Theory [PDF]
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
doaj +2 more sources