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- W2953204957 abstract "A beautiful conjecture of ErdH{o}s-Simonovits and Sidorenko states that if H is a bipartite graph, then the random graph with edge density p has in expectation asymptotically the minimum number of copies of H over all graphs of the same order and edge density. This conjecture also has an equivalent analytic form and has connections to a broad range of topics, such as matrix theory, Markov chains, graph limits, and quasirandomness. Here we prove the conjecture if H has a vertex complete to the other part, and deduce an approximate version of the conjecture for all H. Furthermore, for a large class of bipartite graphs, we prove a stronger stability result which answers a question of Chung, Graham, and Wilson on quasirandomness for these graphs." @default.
- W2953204957 created "2019-06-27" @default.
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- W2953204957 date "2010-04-23" @default.
- W2953204957 modified "2023-09-23" @default.
- W2953204957 title "An approximate version of Sidorenko's conjecture" @default.
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