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arXiv · 2208.12326

Edge-coloured graph homomorphisms, paths, and duality

Kyle Booker·Richard C Brewster
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Abstract

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 $G$ $$ P \to G \Leftrightarrow G \not\to D. $$ The duals are simple to construct, in particular $|V(D)|=|V(P)|-1$.

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Kyle Booker, Richard C Brewster. 2022-08-25. Edge-coloured graph homomorphisms, paths, and duality. https://arxiv.org/abs/2208.12326

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