Complexity of Injective Homomorphisms to Small Tournaments, and of Injective Oriented Colourings
Russell J. Campbell, Nancy E. Clarke, Gary MacGillivray · Open Journal of Discrete Mathematics · 2022
Several possible definitions of local injectivity for a homomorphism of an oriented graph G to an oriented graph H are considered. In each case, we determine the complexity of deciding whether there exists such a homomorphism when G is given and H is a fixed tournament on three or fewer vertices. Each possible definition leads to a locally-injective oriented colouring problem. A dichotomy theorem is proved in each case.