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arXiv · 2505.23384

A large hole in pseudo-random graphs

Sahar Diskin·Michael Krivelevich·Itay Markbreit·Maksim Zhukovskii
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Abstract

We show that there exist constants $δ_1,δ_2>0$ such that if $G$ is an $(n,d,λ)$-graph with $λ/d\leδ_1$, then $G$ contains an induced cycle of length at least $δ_2n/d$. We further demonstrate that, up to a constant factor, this is best possible. Utilising our techniques, we derive that the number of non-isomorphic induced subgraphs of such $G$ is at least exponential in $n\log d/d$, and further demonstrate that this is tight up to a constant factor in the exponent.

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Sahar Diskin, Michael Krivelevich, Itay Markbreit, Maksim Zhukovskii. 2025-05-29. A large hole in pseudo-random graphs. https://arxiv.org/abs/2505.23384

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