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arXiv · 2312.09999

On graphs without cycles of length 0 modulo 4

Ervin Győri·Binlong Li·Nika Salia·Casey Tompkins·Kitti Varga·Manran Zhu
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Abstract

Bollobás proved that for every $k$ and $\ell$ such that $k\mathbb{Z}+\ell$ contains an even number, an $n$-vertex graph containing no cycle of length $\ell \bmod k$ can contain at most a linear number of edges. The precise (or asymptotic) value of the maximum number of edges in such a graph is known for very few pairs $\ell$ and $k$. In this work we precisely determine the maximum number of edges in a graph containing no cycle of length $0 \bmod 4$.

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Ervin Győri, Binlong Li, Nika Salia, Casey Tompkins, Kitti Varga, Manran Zhu. 2023-12-15. On graphs without cycles of length 0 modulo 4. https://arxiv.org/abs/2312.09999

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