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On monochromatic paths in m-coloured tournaments. (English) Zbl 0654.05033
Suppose the arcs of a tournament \(T_ n\) are coloured with m colours in such a way that no subtournament \(T_ 3\) has its arcs coloured with 3 distinct colours. The author shows that such a tournament \(T_ n\) must contain a vertex u that can be reached by a monochromatic path from every other vertex v.
Reviewer: J.W.Moon

MSC:
05C15 Coloring of graphs and hypergraphs
05C20 Directed graphs (digraphs), tournaments
05C38 Paths and cycles
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References:
[1] Sands, B; Sauer, N; Woodrow, R, On monochromatic paths in edge-coloured digraphs, J. combin. theory ser. B, 33, 271-275, (1982) · Zbl 0488.05036
[2] Reid, K.B, Monochromatic reachability, complementary cycles, and single arc reversals in tournaments, (), 11-21 · Zbl 0556.05031
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