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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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On the extremal combinatorics of the hamming space
Journal of Combinatorial Theory - Series A, 1995 In \(n\)-dimensional Hamming space three points are on a line, if they satisfy the triangle inequality with equality. The paper introduces the following problem: How many different points can be found in the Hamming space so that no three of them are on a line (that is they are in general position)? This maximum value is \(A(n)\). The paper surveys the
János Körner
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Treewidth Computation and Extremal Combinatorics [PDF]
Lecture Notes in Computer Science, 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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Problems and results in extremal combinatorics—I
Discrete Mathematics, 2003 Extremal Combinatorics is one of the central areas in Discrete Mathematics. It deals with problems that are often motivated by questions arising in other areas, including Theoretical Computer Science, Geometry and Game Theory.
Dedicated To Miki Simonovits, Noga Alon
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On a Bound in Extremal Combinatorics
Doklady Mathematics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Raigorodskii, A. M., Sagdeev, A. A.
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An Experimental Evaluation of a Function in Extremal Combinatorics
2021 International Conference on Computational Science and Computational Intelligence (CSCI), 2021Kai Wang, Hong Zhang
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Applications of Continuous Combinatorics to Quasirandomness and Extremal Combinatorics
2021The theory of limits of dense combinatorial objects studies the asymptotic behavior of densities of small templates in an increasing sequence of combinatorial objects. The inaugural limit theory of graphons captures limits of graph sequences in a semantic limit object that can be thought of as a fractional version of an adjacency matrix. Since graphons
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Fully Computer-Assisted Proofs in Extremal Combinatorics
Proceedings of the AAAI Conference on Artificial Intelligence, 2023We 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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Some problems in extremal combinatorics
2022My thesis looks into various problems in the field of Extremal Combinatorics. We work on the classical Tur'an problem for graphs before branching out into ``Generalized Tur'an problems". Specifically, we were interested in the growing field of Planar Tur'an problems. We also explore the natural generalization of Tur'an type problems in hypergraphs.
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