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arXiv · 2203.13549

An existence criterion for a cycle such that the vertex set beyond this cycle is independent

Nikolai Karol
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Abstract

We prove that if $G$ is a 2-connected graph with $δ(G) \geqslant \frac{v(G) + 2}{3}$ then $G$ has a cycle $W$ such that $V(G - W)$ is independent. This result is best possible in the sense that it becomes false if $\frac{v(G) + 2}{3}$ is replaced by any smaller number.

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Nikolai Karol. 2022-11-21. An existence criterion for a cycle such that the vertex set beyond this cycle is independent. https://arxiv.org/abs/2203.13549

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