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Colourings of $(m, n)$-coloured mixed graphs

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arxiv 2010.09091 v3 pith:D6NA33F2 submitted 2020-10-18 math.CO cs.DM

classification math.COcs.DM
keywords graphsmixedcolouredcolouringsgraphorientedvertexassigned
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abstract

A mixed graph is, informally, an object obtained from a simple undirected graph by choosing an orientation for a subset of its edges. A mixed graph is $(m, n)$-coloured if each edge is assigned one of $m \geq 0$ colours, and each arc is assigned one of $n \geq 0$ colours. Oriented graphs are $(0, 1)$-coloured mixed graphs, and 2-edge-coloured graphs are $(2, 0)$-coloured mixed graphs. We show that results of Sopena for vertex colourings of oriented graphs, and of Kostochka, Sopena and Zhu for vertex colourings oriented graphs and 2-edge-coloured graphs, are special cases of results about vertex colourings of $(m, n)$-coloured mixed graphs. Both of these can be regarded as a version of Brooks' Theorem.

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Cited by 2 Pith papers

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