Monochromatic Paths and at Most 2-Coloured Arc Sets in Edge-Coloured Tournaments

@article{GaleanaSnchez2005MonochromaticPA,
  title={Monochromatic Paths and at Most 2-Coloured Arc Sets in Edge-Coloured Tournaments},
  author={Hortensia Galeana-S{\'a}nchez and Roc{\'i}o Rojas-Monroy},
  journal={Graphs and Combinatorics},
  year={2005},
  volume={21},
  pages={307-317}
}
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… CONTINUE READING

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