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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: [email protected]; [email protected]
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: [email protected]; [email protected]
MATHIAS SCHACHT
Affiliation:
Fachbereich Mathematik, Bundesstra SSe 55, Universität Hamburg, Hamburg, 20146 Germany. e-mail: [email protected]
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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

REFERENCES

[1] Bal, D. and DeBiasio, L. Partitioning random graphs into monochromatic components. Electron. J. Combin. 24 (2017), no. 1, Paper 1.18, 25 pages. MR3609188.Google Scholar
[2] Bollobás, B. Modern graph theory. Graduate Texts in Math. vol. 184 (Springer-Verlag, New York, 1998). MR1633290.Google Scholar
[3] Bollobás, B. Random graphs, 2nd ed. Cambridge Stud. Adv. Math. vol. 73 (Cambridge University Press, Cambridge, 2001). MR1864966.Google Scholar
[4] Bondy, J. A. and Murty, U. S. R. Graph theory. Graduate Texts in Math. vol. 244 (Springer, New York, 2008). MR2368647.Google Scholar
[5] Diestel, R. Graph theory, 5th ed. Graduate Texts in Math. vol. 173 (Springer, Berlin, 2017). MR3644391.Google Scholar
[6] Ebsen, O., Mota, G. O. and Schnitzer, J. Personal communication, 2017.Google Scholar
[7] Friedgut, E. Sharp thresholds of graph properties, and the k-sat problem. J. Amer. Math. Soc. 12 (1999), no. 4, 1017–1054, DOI 10.1090/S0894-0347-99-00305-7. With an appendix by Jean Bourgain. MR1678031.Google Scholar
[8] Janson, S., Łuczak, T. and Ruciński, A. Random graphs. Wiley-Interscience Series in Discrete Mathematics and Optimization (Wiley-Interscience, New York, 2000). MR1782847.Google Scholar