arXiv:1904.07219 [math.CO]AbstractReferencesReviewsResources
The Turán number of blow-ups of trees
Andrzej Grzesik, Oliver Janzer, Zoltán Lóránt Nagy
Published 2019-04-15Version 1
A conjecture of Erd\H{o}s 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 generalise many previously proven cases of the Erd\H{o}s conjecture, including the related results of F\"uredi and Alon, Krivelevich and Sudakov. Our proof uses supersaturation and a random walk on an auxiliary graph.
Categories: math.CO
Related articles: Most relevant | Search more
arXiv:1309.3936 [math.CO] (Published 2013-09-13)
A new proof of Andrews' conjecture for $_4φ_3$-series
Proof of a conjecture of Hadwiger
Another proof of Wilmes' conjecture