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Monochromatic trees in random graphs

Published online by Cambridge University Press:  16 January 2018

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

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
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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[7] Friedgut, E. Sharp thresholds of graph properties, and the k-sat problem. J. Amer. Math. Soc. 12 (1999), no. 4, 10171054, DOI 10.1090/S0894-0347-99-00305-7. With an appendix by Jean Bourgain. MR1678031.CrossRefGoogle Scholar
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