Colourings of $(m, n)$-coloured mixed graphs
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)...
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| Veröffentlicht in: | Discrete mathematics and theoretical computer science Jg. 25:2; H. Graph Theory |
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| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Discrete Mathematics & Theoretical Computer Science
09.01.2025
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| Schlagworte: | |
| ISSN: | 1365-8050, 1365-8050 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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.
Comment: 7 pages, no figures |
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| ISSN: | 1365-8050 1365-8050 |
| DOI: | 10.46298/dmtcs.6848 |