A dichotomy theorem for Γ-switchable H-colouring on m-edge coloured graphs

06/09/2023

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by   Richard Brewster, et al.

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Let G be a graph in which each edge is assigned one of the colours 1, 2, …, m, and let Γ be a subgroup of S_m. The operation of switching at a vertex x of G with respect to an element π of Γ permutes the colours of the edges incident with x according to π. 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 Γ acts transitively.