Sparse halves in $K_4$-free graphs

Xizhi Liu; Jie Ma

Sparse halves in $K_4$-free graphs

Combinatorics 2020-07-30 v1

Authors: Xizhi Liu , Jie Ma

Abstract

A conjecture of Chung and Graham states that every $K_4$ -free graph on $n$ vertices contains a vertex set of size $\lfloor n/2 \rfloor$ that spans at most $n^2/18$ edges. We make the first step toward this conjecture by showing that it holds for all regular graphs.

Keywords

hadwiger conjecture graph theory graph cycles

Cite

@article{arxiv.2007.14623,
  title  = {Sparse halves in $K_4$-free graphs},
  author = {Xizhi Liu and Jie Ma},
  journal= {arXiv preprint arXiv:2007.14623},
  year   = {2020}
}

Comments

19 pages including 3 pages appendix

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