Monochromatic trees in random graphs
Combinatorics
2019-02-20 v2
Abstract
Bal and DeBiasio [Partitioning random graphs into monochromatic components, Electron. J. Combin. 24 (2017), Paper 1.18] put forward a conjecture concerning the threshold for the following Ramsey-type property for graphs : every -colouring of the edge set of yields pairwise vertex disjoint monochromatic trees that partition the whole vertex set of . We determine the threshold for this property for two colours.
Keywords
Cite
@article{arxiv.1611.10299,
title = {Monochromatic trees in random graphs},
author = {Yoshiharu Kohayakawa and Guilherme Oliveira Mota and Mathias Schacht},
journal= {arXiv preprint arXiv:1611.10299},
year = {2019}
}
Comments
23 pages, second version addresses changes arising from the referee reports and we added a section showing that the main result does not extend straightforwardly to more than two colours