1 research outputs found
King-serf duo by monochromatic paths in k-edge-coloured tournaments
An open conjecture of Erd\H{o}s states that for every positive integer
there is a (least) positive integer so that whenever a tournament has
its edges colored with colors, there exists a set of at most
vertices so that every vertex has a monochromatic path to some point in . We
consider a related question and show that for every (finite or infinite)
cardinal there is a cardinal such that in every
-edge-coloured tournament there exist disjoint vertex sets with
total size at most so that every vertex has a
monochromatic path of length at most two from to or from to .Comment: 5 page