Geodesic
Colourings of $(m, n)$-coloured mixed graphs
Discrete mathematics & theoretical computer science, Tome 25 (2023-2024) no. 2.

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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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     title = {Colourings of $(m, n)$-coloured mixed graphs},
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MacGillivray, Gary; Nasserasr, Shahla; Yang, Feiran. Colourings of $(m, n)$-coloured mixed graphs. Discrete mathematics & theoretical computer science, Tome 25 (2023-2024) no. 2. doi : 10.46298/dmtcs.6848. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6848/

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