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.
متن کاملMonochromatic paths and monochromatic sets of arcs in bipartite tournaments
We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours and all of them are used. A directed path is called monochromatic if all of its arcs are coloured alike. A set N of vertices of D is called a kernel by monochromatic paths if for every pair of vertices there is no monochromatic path between them and for every vertex v in V (D) \ N there is a monochromatic p...
متن کاملTournaments with kernels by monochromatic paths
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...
متن کاملOn monochromatic paths and bicolored subdigraphs in arc-colored tournaments
Consider an arc-colored digraph. A set of vertices N is a kernel by monochromatic paths if all pairs of distinct vertices of N have no monochromatic directed path between them and if for every vertex v not in N there exists n ∈ N such that there is a monochromatic directed path from v to n. In this paper we prove different sufficient conditions which imply that an arc-colored tournament has a k...
متن کاملOn monochromatic paths and monochromatic 4-cycles in edge coloured bipartite tournaments
We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours. A directed path (or a directed cycle) is called monochromatic if all of its arcs are coloured alike. A set N ⊆ V (D) is said to be a kernel by monochromatic paths if it satis5es the following two conditions: (i) For every pair of di7erent vertices u, v∈N , there is no monochromatic directed path between th...
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ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2017
ISSN: 1571-0653
DOI: 10.1016/j.endm.2017.06.036