Edge-coloured graph homomorphisms, paths, and duality

08/25/2022

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by   Kyle Booker, et al.

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We present a edge-coloured analogue of the duality theorem for transitive tournaments and directed paths. Given a edge-coloured path P whose edges alternate blue and red, we construct a edge-coloured graph D so that for any edge-coloured graph G P → G ⇔ G ↛D. The duals are simple to construct, in particular |V(D)|=|V(P)|-1.