The confirmation of a conjecture on disjoint cycles in a graph

Fuhong Ma; Jin Yan

The confirmation of a conjecture on disjoint cycles in a graph

Combinatorics 2017-07-11 v1

Authors: Fuhong Ma , Jin Yan

Abstract

In this paper, we prove the following conjecture proposed by Gould, Hirohata and Keller [Discrete Math. submitted]: Let $G$ be a graph of sufficiently large order. If $\sigma_t(G) \geq 2kt - t + 1$ for any two integers $k \geq 2$ and $t \geq 5$ , then $G$ contains $k$ disjoint cycles.

Keywords

disjoint cycles graph theory degree sum condition Gould-Hirohata-Keller conjecture sufficiently large order

Cite

@article{arxiv.1707.02390,
  title  = {The confirmation of a conjecture on disjoint cycles in a graph},
  author = {Fuhong Ma and Jin Yan},
  journal= {arXiv preprint arXiv:1707.02390},
  year   = {2017}
}

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