King-Serf Duo by Monochromatic Paths in k-Edge-Coloured Tournaments
نویسندگان
چکیده
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 cardinal λκ such that in every κ-edge-coloured tournament there exist disjoint vertex sets K,S with total size at most λκ so that every vertex v has a monochromatic path of length at most two from K to v or from v to S.
منابع مشابه
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عنوان ژورنال:
- Electr. J. Comb.
دوره 24 شماره
صفحات -
تاریخ انتشار 2017