An approximate version of Sumner's universal tournament conjecture

作者：Kuehn Daniela; Mycroft Richard; Osthus Deryk

来源：Journal of Combinatorial Theory - Series B, 2011, 101(6): 415-447.

DOI：10.1016/j.jctb.2010.12.006

• Trees
• Tournaments
• Digraphs
• Regularity lemma

Sumner's universal tournament conjecture states that any tournament on 2n - 2 vertices contains a copy of any directed tree on n vertices. We prove an asymptotic version of this conjecture, namely that any tournament on (2 + o(1))n vertices contains a copy of any directed tree on n vertices. In addition, we prove an asymptotically best possible result for trees of bounded degree, namely that for any fixed Delta, any tournament on (1 + o(1))n vertices contains a copy of any directed tree on n vertices with maximum degree at most Delta.

• 出版日期2011-11