Speaker: Andrzej Grzesik
Title:
Turán problem for degenerated graph

Abstract:
A conjecture of Erdős from 1967 asserts that any graph on n vertices which does not contain a fixed r-degenerate bipartite graph F has at most Cn^{2−1/r} edges, where C is a constant depending only on F. We show that this bound holds for a large family of r-degenerate bipartite graphs, including all r-degenerate blow-ups of trees. Our results generalize many previously proven cases of the Erdős conjecture, including the related results of Füredi and Alon, Krivelevich and Sudakov. Joint work with Oliver Janzér and Zoltán Lóránt Nagy.
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