A proof of Sumner's universal tournament conjecture for large tournaments
نویسندگان
چکیده
Sumner’s universal tournament conjecture states that any tournament on 2n−2 vertices contains any directed tree on n vertices. In this paper we prove that this conjecture holds for all sufficiently large n. The proof makes extensive use of results and ideas from a recent paper by the same authors, in which an approximate version of the conjecture was
منابع مشابه
Median orders of tournaments: A tool for the second neighborhood problem and Sumner's conjecture
We give a short constructive proof of a theorem of Fisher: every tournament contains a vertex whose second outneighborhood is as large as its ®rst outneighborhood. Moreover, we exhibit two such vertices provided that the tournament has no dominated vertex. The proof makes use of median orders. A second application of median orders is that every tournament of order 2nÿ 2 contains every arboresce...
متن کاملMedian orders of tournaments: a tool for the second neighbourhood problem and Sumner’s conjecture
We give a short constructive proof of a theorem of Fisher: every tournament contains a vertex whose second outneighbourhood is as large as its first outneighbourhood. Moreover, we exhibit two such vertices provided that the tournament has no dominated vertex. The proof makes use of median orders. A second application of median orders is that every tournament of order 2n − 2 contains every arbor...
متن کاملDisjoint 3-Cycles in Tournaments: A Proof of The Bermond-Thomassen Conjecture for Tournaments
We prove that every tournament with minimum out-degree at least 2k− 1 contains k disjoint 3-cycles. This provides additional support for the conjecture by Bermond and Thomassen that every digraph D of minimum out-degree 2k − 1 contains k vertex disjoint cycles. We also prove that for every > 0, when k is large enough, every tournament with minimum out-degree at least (1.5+ )k contains k disjoin...
متن کاملDisjoint 3 - cycles in tournaments : a proof of the 1 Bermond - Thomassen conjecture for tournaments ∗
5 We prove that every tournament with minimum out-degree at least 2k− 1 contains k disjoint 6 3-cycles. This provides additional support for the conjecture by Bermond and Thomassen that 7 every digraph D of minimum out-degree 2k − 1 contains k vertex disjoint cycles. We also prove 8 that for every > 0, when k is large enough, every tournament with minimum out-degree at least 9 (1.5+ )k contains...
متن کاملColoring tournaments with forbidden substructures
Coloring graphs is an important algorithmic problem in combinatorics with many applications in computer science. In this paper we study coloring tournaments. A chromatic number of a random tournament is of order Ω( n log(n)). The question arises whether the chromatic number can be proven to be smaller for more structured nontrivial classes of tournaments. We analyze the class of tournaments def...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Electronic Notes in Discrete Mathematics
دوره 38 شماره
صفحات -
تاریخ انتشار 2011