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 , in any -edge-colouring of the random graph 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.
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