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

Nikolai Karol

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

Combinatorics 2022-11-23 v3

Authors: Nikolai Karol

Abstract

We prove that if $G$ is a 2-connected graph with $\delta(G) \geqslant \frac{v(G) + 2}{3}$ 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.

Keywords

2-connected graph minimum degree cycle independent set extremal graph theory

Cite

@article{arxiv.2203.13549,
  title  = {An existence criterion for a cycle such that the vertex set beyond this cycle is independent},
  author = {Nikolai Karol},
  journal= {arXiv preprint arXiv:2203.13549},
  year   = {2022}
}

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