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arXiv · 1611.10299

Monochromatic trees in random graphs

Yoshiharu Kohayakawa·Guilherme Oliveira Mota·Mathias Schacht
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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 $G$: every $k$-colouring of the edge set of $G$ yields $k$ pairwise vertex disjoint monochromatic trees that partition the whole vertex set of $G$. We determine the threshold for this property for two colours.

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Yoshiharu Kohayakawa, Guilherme Oliveira Mota, Mathias Schacht. 2017-10-30. Monochromatic trees in random graphs. https://doi.org/10.1017/s0305004117000846

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