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Monochromatic trees in random graphs

Published online by Cambridge University Press:  16 January 2018

YOSHIHARU KOHAYAKAWA ,
GUILHERME OLIVEIRA MOTA  and
MATHIAS SCHACHT
YOSHIHARU KOHAYAKAWA
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010 05508-090 São Paulo, São Paulo, Brazil. e-mail: yoshi@ime.usp.br; mota@ime.usp.br
GUILHERME OLIVEIRA MOTA
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010 05508-090 São Paulo, São Paulo, Brazil. e-mail: yoshi@ime.usp.br; mota@ime.usp.br
MATHIAS SCHACHT
Affiliation:
Fachbereich Mathematik, Bundesstra SSe 55, Universität Hamburg, Hamburg, 20146 Germany. e-mail: schacht@math.uni-hamburg.de
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 166 , Issue 1 , January 2019 , pp. 191 - 208
Copyright
Copyright © Cambridge Philosophical Society 2018 

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Footnotes

The collaboration of the authors was supported by CAPES/DAAD PROBRAL (Proc. 430/15) and by FAPESP (Proc. 2013/03447-6).

‡

Partially supported by FAPESP (Proc. 2013/03447-6, 2013/07699-0), by CNPq (Proc. 459335/2014-6, 310974/2013-5) and by Project MaCLinC/USP.

§

Supported by FAPESP (Proc. 2013/11431-2, 2013/20733-2) and partially by CNPq (Proc. 459335/2014-6).

References

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