A Ramsey type result for oriented trees

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Abstract

Given positive integers h and k, denote by r(h,k) the smallest integer n such that in any k-coloring of the edges of a tournament on more than n vertices there is a monochromatic copy of every oriented tree on h vertices. We prove that r(h,k)=(h−1)k for all k sufficiently large (k=Θ(hlogh) suffices). The bound (h−1)k is tight. The related parameter r(h,k) where some color contains all oriented trees is asymptotically determined. Values of r(h,2) for some small h are also established.

Original languageEnglish
Pages (from-to)1-9
Number of pages9
JournalEuropean Journal of Combinatorics
Volume60
DOIs
StatePublished - 1 Feb 2017

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Ltd

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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