On 3-coloured tournaments
نویسندگان
چکیده
We (re-)prove that in every 3-edge-coloured tournament in which no vertex is incident with all colours there is either a cyclic rainbow triangle or a vertex dominating every other vertex monochromatically.
منابع مشابه
A counterexample to a conjecture on edge-coloured tournaments
We call the tournament T an m-coloured tournament if the arcs of T are coloured with m colours. In this paper we prove that for each n¿ 6, there exists a 4-coloured tournament Tn of order n satisfying the two following conditions: (1) Tn does not contain C3 (the directed cycle of length 3, whose arcs are coloured with three distinct colours), and (2) Tn does not contain any vertex v such that f...
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 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...
متن کاملMonochromatic paths and quasi-monochromatic 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 directed cycle is called quasi-monochromatic if with at most one exception all of its arcs are coloured alike. A set N ⊆ V (D) is said to be a kernel by monochromatic paths if it satisfies the following t...
متن کاملKing-Serf Duo by Monochromatic Paths in k-Edge-Coloured Tournaments
An open conjecture of Erdős states that for every positive integer k there is a (least) positive integer f(k) so that whenever a tournament has its edges colored with k colors, there exists a set S of at most f(k) vertices so that every vertex has a monochromatic path to some point in S. We consider a related question and show that for every (finite or infinite) cardinal κ > 0 there is a cardin...
متن کامل