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arXiv · 2106.00597

The largest hole in sparse random graphs

Nemanja Draganić·Stefan Glock·Michael Krivelevich
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Abstract

We show that for any $d=d(n)$ with $d_0(ε) \le d =o(n)$, with high probability, the size of a largest induced cycle in the random graph $G(n,d/n)$ is $(2\pm ε)\frac{n}{d}\log d$. This settles a long-standing open problem in random graph theory.

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Nemanja Draganić, Stefan Glock, Michael Krivelevich. 2022-02-28. The largest hole in sparse random graphs. https://arxiv.org/abs/2106.00597

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