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arXiv · 1809.04675

The Simple Chromatic Number of $(m,n)$-Mixed Graphs

Christopher Duffy·Jarrod Pas
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Abstract

An $(m,n)$-mixed graph generalizes the notions of oriented graphs and edge-coloured graphs to a graph object with $m$ arc types and $n$ edge types. A simple colouring of such a graph is a non-trivial homomorphism to a reflexive target. We find that simple chromatic number of complete $(m,n)$-mixed graphs can be found in polynomial time. For planar graphs and $k$-trees ($k \geq 3$) we find that allowing the target to be reflexive does not lower the chromatic number of the respective family of $(m,n)$-mixed graphs. This implies that the search for universal targets for such families may be restricted to simple cliques.

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Christopher Duffy, Jarrod Pas. 2018-09-12. The Simple Chromatic Number of $(m,n)$-Mixed Graphs. https://arxiv.org/abs/1809.04675

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