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Rational exponents near two
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abstract
A longstanding conjecture of Erd\H{o}s and Simonovits states that for every rational $r$ between $1$ and $2$ there is a graph $H$ such that the largest number of edges in an $H$-free graph on $n$ vertices is $\Theta(n^r)$. Answering a question raised by Jiang, Jiang and Ma, we show that the conjecture holds for all rationals of the form $2 - a/b$ with $b$ sufficiently large in terms of $a$.
Forward citations
Cited by 2 Pith papers
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Recent progress in graph theory using expansion
Sublinear expansion—weak neighbourhood growth in sparse graphs—has resolved many long-standing extremal graph theory conjectures, and this survey organizes that progress.
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