An Approximate Form of Sidorenko's Conjecture

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• David Conlon (St John's College, Cambridge)
• Thursday 03 February 2011, 15:00-16:00
• MR12.

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A beautiful conjecture of Erdos-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. 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.

Joint work with Jacob Fox and Benny Sudakov.

This talk is part of the Combinatorics Seminar series.

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