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Seunghun Lee (이승훈), Leray numbers of complexes of graphs with bounded matching number
Seunghun Lee (이승훈), Leray numbers of complexes of graphs with bounded matching number
Given a graph
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Discrete Math Seminar
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Eun Jung Kim (김은정), Twin-width: tractable FO model checking
Eun Jung Kim (김은정), Twin-width: tractable FO model checking
Inspired by a width invariant defined on permutations by Guillemot and Marx , we introduce the notion of twin-width on graphs and on matrices. Proper minor-closed classes, bounded rank-width graphs, map graphs,
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O-joung Kwon (권오정), Mim-width: a width parameter beyond rank-width
O-joung Kwon (권오정), Mim-width: a width parameter beyond rank-width
Vatshelle (2012) introduced a width parameter called mim-width. It is based on the following cut function : for a vertex partition (A,B) of a graph, the complexity of this partition is computed by the size of a maximum induced matching of the bipartite subgraph induced by edges between A and B. This parameter naturally extends …
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Hong Liu (刘鸿), Asymptotic Structure for the Clique Density Theorem
Hong Liu (刘鸿), Asymptotic Structure for the Clique Density Theorem
The famous Erdős-Rademacher problem asks for the smallest number of r-cliques in a graph with the given number of vertices and edges. Despite decades of active attempts, the asymptotic value of this extremal function for all r was determined only recently, by Reiher . Here we describe the asymptotic structure of all almost extremal graphs. …
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Huy-Tung Nguyen, The average cut-rank of graphs
Huy-Tung Nguyen, The average cut-rank of graphs
The cut-rank of a set X of vertices in a graph G is defined as the rank of the X×(V(G)∖X) matrix over the binary field whose (i,j)-entry is 1 if the vertex i in X is adjacent to the vertex j in V(G)∖X and 0 otherwise. We introduce the graph parameter called the average cut-rank …