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Monochromatic trees in random tournaments

Part of: Graph theory

Published online by Cambridge University Press:  07 November 2019

Matija Bucić ,
Sven Heberle ,
Shoham Letzter  and
Benny Sudakov
Matija Bucić
Affiliation:
Department of Mathematics, ETH Zürich, Raemistrasse 101, 8092 Zürich, Switzerland
Sven Heberle
Affiliation:
Department of Mathematics, ETH Zürich, Raemistrasse 101, 8092 Zürich, Switzerland
Shoham Letzter
Affiliation:
ETH Institute for Theoretical Studies, ETH Zürich, Clausiusstrasse 47, 8092 Zürich, Switzerland
Benny Sudakov*
Affiliation:
Department of Mathematics, ETH Zürich, Raemistrasse 101, 8092 Zürich, Switzerland
*
*Corresponding author. Email: benjamin.sudakov@math.ethz.ch
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Abstract

We prove that, with high probability, in every 2-edge-colouring of the random tournament on n vertices there is a monochromatic copy of every oriented tree of order $O(n{\rm{/}}\sqrt {{\rm{log}} \ n} )$. This generalizes a result of the first, third and fourth authors, who proved the same statement for paths, and is tight up to a constant factor.

MSC classification

Primary: 05C05: Trees
Secondary: 05C55: Generalized Ramsey theory 05C80: Random graphs
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 29 , Issue 3 , May 2020 , pp. 318 - 345
Copyright
© Cambridge University Press 2019

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Footnotes

†

Research supported by Dr Max Rössler, the Walter Haefner Foundation and the ETH Zurich Foundation.

‡

Research supported in part by SNSF grant 200021-175573.

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