Abstract
We call the tournament T an m-coloured tournament if the arcs of T are coloured with m-colours. If v is a vertex of an m-coloured tournament T, we denote by ξ(v) the set of colours assigned to the arcs with v as an endpoint.In this paper is proved that if T is an m-coloured tournament with |ξ(v)|≤2 for each vertex v of T, and T satisfies at least one of the two following properties (1) m≠3 or (2) m=3 and T contains no C3 (the directed cycle of length 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 directed path from x to v.
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