2022/08/25 by Kyle Booker, Booker, Kyle, Richard C. Brewster +1
Computer Science · Mathematics · #05C15 #05C60 #68R10 #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2208.12326
openalex publication_date 2022/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \not→ D. The duals are simple to construct, in particular |V(D)|=|V(P)|-1.