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Unavoidable trees in tournaments
Author(s) -
Mycroft Richard,
Naia Tássio
Publication year - 2018
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20765
Subject(s) - tournament , combinatorics , conjecture , mathematics , tree (set theory) , degree (music) , discrete mathematics , physics , acoustics
An oriented tree T on n vertices is unavoidable if every tournament on n vertices contains a copy of T . In this paper, we give a sufficient condition for T to be unavoidable, and use this to prove that almost all labeled oriented trees are unavoidable, verifying a conjecture of Bender and Wormald. We additionally prove that every tournament on n + o ( n ) vertices contains a copy of every oriented tree T on n vertices with polylogarithmic maximum degree, improving a result of Kühn, Mycroft, and Osthus.