A large hole in pseudo-random graphs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910973725507584 |
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| author | Diskin, Sahar Krivelevich, Michael Markbreit, Itay Zhukovskii, Maksim |
| author_facet | Diskin, Sahar Krivelevich, Michael Markbreit, Itay Zhukovskii, Maksim |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_23384 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A large hole in pseudo-random graphs Diskin, Sahar Krivelevich, Michael Markbreit, Itay Zhukovskii, Maksim Combinatorics Probability 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. |
| title | A large hole in pseudo-random graphs |
| topic | Combinatorics Probability |
| url | https://arxiv.org/abs/2505.23384 |