随机比赛中的单色树

Combinatorics, Probability and Computing Pub Date : 2018-09-19 DOI:10.1017/S0963548319000373

Matija Bucić, Sven Heberle, Shoham Letzter, B. Sudakov

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引用次数: 1

摘要

摘要:我们证明了在n个顶点的随机竞赛的每一个2边着色中，有很大的概率存在一个阶$O(n{\rm{/}}\sqrt {{\rm{log}} \ n})$的每个有向树的单色副本。这推广了第一，第三和第四作者的结果，他们证明了路径的相同陈述，并且紧密到一个常数因子。

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Monochromatic trees in random tournaments

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.

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Combinatorics, Probability and Computing

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