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arXiv · 2306.05962

A dichotomy theorem for $\Gamma$-switchable $H$-colouring on $m$-edge coloured graphs

Richard Brewster·Arnott Kidner·Gary MacGillivray
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Abstract

Let $G$ be a graph in which each edge is assigned one of the colours $1, 2, \ldots, m$, and let $\Gamma$ be a subgroup of $S_m$. The operation of switching at a vertex $x$ of $G$ with respect to an element $\pi$ of $\Gamma$ permutes the colours of the edges incident with $x$ according to $\pi$. We investigate the complexity of whether there exists a sequence of switches that transforms a given $m$-edge coloured graph $G$ so that it has a colour-preserving homomorphism to a fixed $m$-edge coloured graph $H$ and give a dichotomy theorem in the case that $\Gamma$ acts transitively.

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Richard Brewster, Arnott Kidner, Gary MacGillivray. 2023-06-09. A dichotomy theorem for $\Gamma$-switchable $H$-colouring on $m$-edge coloured graphs. https://arxiv.org/abs/2306.05962

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