A conjecture of Verstraëte on vertex-disjoint cycles

Jun Gao; Jie Ma

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arXiv · 1906.03206

A conjecture of Verstraëte on vertex-disjoint cycles

Jun Gao·Jie Ma

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Abstract

Answering a question of Häggkvist and Scott, Verstraëte proved that every sufficiently large graph with average degree at least $k^2+19k+10$ contains $k$ vertex-disjoint cycles of consecutive even lengths. He further conjectured that the same holds for every graph $G$ with average degree at least $k^2+3k+2$. In this paper we prove this conjecture for $k\geq 19$ when $G$ is sufficiently large. We also show that for any $ε>0$ and large $k\geq k_ε$, average degree at least $k^2+3k-2+ε$ suffices, which is asymptotically tight for infinitely many graphs.

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BibTeX RIS

Jun Gao, Jie Ma. 2019-06-07. A conjecture of Verstraëte on vertex-disjoint cycles. https://arxiv.org/abs/1906.03206

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