Obstructions to some injective oriented colourings

Authors

• Russell J. Campbell, University of the Fraser ValleyFollow
• Nancy E. Clarke, Acadia UniversityFollow
• Gary MacGillivray, University of VictoriaFollow

Abstract

Each of several possible definitions of local injectivity for a homomorphism of an oriented graph $G$ to an oriented graph $H$ leads to an injective oriented colouring problem. For each case in which such a problem is solvable in polynomial time, we identify a set $\mathcal{F}$ of oriented graphs such that an oriented graph $G$ has an injective oriented colouring with the given number of colours if and only if there is no $F \in \mathcal{F}$ for which there is a locally-injective homomorphism of $F$ to $G$.

Recommended Citation

Campbell, Russell J.; Clarke, Nancy E.; and MacGillivray, Gary (2026) "Obstructions to some injective oriented colourings," Theory & Applications of Graphs: Vol. 13: Iss. 1, Article 5.
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol13/iss1/5