Monochromatic paths in random tournaments
نویسندگان
چکیده
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.
منابع مشابه
Monochromatic 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...
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ورودعنوان ژورنال:
- Electronic Notes in Discrete Mathematics
دوره 61 شماره
صفحات -
تاریخ انتشار 2017