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- W2938574626 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 generalise many previously proven cases of the Erdős conjecture, including the related results of Furedi and Alon, Krivelevich and Sudakov. Our proof uses supersaturation and a random walk on an auxiliary graph." @default.
- W2938574626 created "2019-04-25" @default.
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- W2938574626 date "2019-04-15" @default.
- W2938574626 modified "2023-09-27" @default.
- W2938574626 title "The Tur'an number of blow-ups of trees" @default.
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