A remark on Hamilton cycles with few colors

Igor Balla; Alexey Pokrovskiy; Benny Sudakov

A remark on Hamilton cycles with few colors

Combinatorics 2017-06-16 v1

Authors: Igor Balla , Alexey Pokrovskiy , Benny Sudakov

Abstract

Akbari, Etesami, Mahini, and Mahmoody conjectured that every proper edge colouring of $K_n$ with $n$ colours contains a Hamilton cycle with $\leq O(\log n)$ colours. They proved that there is always a Hamilton cycle with $\leq 8\sqrt n$ colours. In this note we improve this bound to $O(\log^3 n)$ .

Keywords

Hamilton cycles edge coloring complete graphs combinatorial conjectures upper bounds graph theory

Cite

@article{arxiv.1706.04903,
  title  = {A remark on Hamilton cycles with few colors},
  author = {Igor Balla and Alexey Pokrovskiy and Benny Sudakov},
  journal= {arXiv preprint arXiv:1706.04903},
  year   = {2017}
}

Related papers

View all related →