TITLE:
Complexity of Injective Homomorphisms to Small Tournaments, and of Injective Oriented Colourings
AUTHORS:
Russell J. Campbell, Nancy E. Clarke, Gary MacGillivray
KEYWORDS:
Injective Graph Homomorphism, Oriented Colouring, Complexity
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.13 No.1,
November
9,
2022
ABSTRACT: 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.