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Counting tree-like graphs in locally dense graphs
[2018 Discrete Math 세미나 ]
Date: 2018-01-08
Speaker : Joonkyung Lee (Mathematical Institute, University of Oxford, Oxford, UK)
Abstract : We prove that a class of graphs obtained by gluing complete multipartite graphs in a tree-like way satisfies a conjecture of Kohayakawa, Nagle, Rödl, and Schacht on random-like counts for small graphs in locally dense graphs. This implies an approximate version of the conjecture for graphs with bounded tree-width. We also prove an analogous result for odd cycles instead of complete multipartite graphs. The proof uses a general information theoretic method to prove graph homomorphism inequalities for tree-like structured graphs, which may be of independent interest.
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