English

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 GG: every kk-colouring of the edge set of GG yields kk pairwise vertex disjoint monochromatic trees that partition the whole vertex set of GG. 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

R2 v1 2026-06-22T17:09:45.563Z