Edge-coloured graph homomorphisms, paths, and duality
Kyle Booker, Richard C Brewster

TL;DR
This paper introduces an edge-coloured analogue of the duality theorem for directed paths and tournaments, establishing a correspondence between edge-coloured paths and graphs via homomorphisms, with simple dual constructions.
Contribution
It extends the duality theorem to edge-coloured graphs, providing explicit constructions for duals of edge-coloured paths and related graphs.
Findings
Established a duality between edge-coloured paths and graphs.
Provided explicit, simple constructions for dual graphs.
Demonstrated the applicability to edge-coloured transitive tournaments.
Abstract
We present a edge-coloured analogue of the duality theorem for transitive tournaments and directed paths. Given a edge-coloured path whose edges alternate blue and red, we construct a edge-coloured graph so that for any edge-coloured graph The duals are simple to construct, in particular .
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Taxonomy
TopicsAdvanced Graph Theory Research · Rings, Modules, and Algebras · Advanced Topology and Set Theory
