Monochromatic trees in random tournaments
نویسندگان
چکیده
منابع مشابه
Monochromatic paths in random tournaments
We prove that, with high probability, any 2-edge-colouring of a random tournament on n vertices contains a monochromatic path of length Ω(n/ √ log n). This resolves a conjecture of Ben-Eliezer, Krivelevich and Sudakov and implies a nearly tight upper bound on the oriented size Ramsey number of a directed path.
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Let D be a digraph, and C a (not necessarily directed) cycle in D; an obstruction of C is a vertex x of C such that the outdegree in C of x is 2, that is, δ C (x) = 2. We will denote by Ω(C) the number of obstructions of C and by lΩ(C) the Ω-length of C, which is defined by lΩ(C) = |V (C)| − |Ω(C)|. An Ω-pseudodiagonal of C is an arc in A(D) \ A(C) with both vertices in C and whose initial vert...
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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2019
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548319000373