English

Covering $3$-edge-coloured random graphs with monochromatic trees

Combinatorics 2020-06-26 v1

Abstract

We investigate the problem of determining how many monochromatic trees are necessary to cover the vertices of an edge-coloured random graph. More precisely, we show that for pn1/6(lnn)1/6p\gg n^{-1/6}{(\ln n)}^{1/6}, in any 33-edge-colouring of the random graph G(n,p)G(n,p) we can find three monochromatic trees such that their union covers all vertices. This improves, for three colours, a result of Buci\'c, Kor\'andi and Sudakov.

Keywords

Cite

@article{arxiv.2006.14469,
  title  = {Covering $3$-edge-coloured random graphs with monochromatic trees},
  author = {Yoshiharu Kohayakawa and Walner Mendonça and Guilherme Oliveira Mota and Bjarne Schülke},
  journal= {arXiv preprint arXiv:2006.14469},
  year   = {2020}
}

Comments

16 pages, 5 figures

R2 v1 2026-06-23T16:37:37.155Z