English

On the anti-Ramsey numbers of linear forests

Combinatorics 2020-03-18 v1

Abstract

For a fixed graph FF, the anti-Ramsey number\textit{anti-Ramsey number}, AR(n,F)AR(n,F), is the maximum number of colors in an edge-coloring of KnK_n which does not contain a rainbow copy of FF. In this paper, we determine the exact value of anti-Ramsey numbers of linear forests for sufficiently large nn, and show the extremal edge-colored graphs. This answers a question of Fang, Gy\H{o}ri, Lu and Xiao.

Keywords

Cite

@article{arxiv.2003.07541,
  title  = {On the anti-Ramsey numbers of linear forests},
  author = {Tian-Ying Xie and Long-Tu Yuan},
  journal= {arXiv preprint arXiv:2003.07541},
  year   = {2020}
}