On monochromatic paths in m-coloured tournaments

AbstractWe call the tournament T an m-coloured tournament if the arcs of T are coloured with m colours. In this paper we have proved that if T is an m-coloured tournament which does not contain any tournament of order 3 whose arcs are coloured with three distinct colours then there is a vertex v of T such that for every other vertex x of T there is a monochromatic path from x to v