Author(s)

Russell J. Campbell¹, Nancy E. Clarke², Gary MacGillivray³

¹University of the Fraser Valley, Abbotsford, British Columbia.
²Acadia University, Wolfville, Nova Scotia.
³University of Victoria, Victoria, British Columbia.

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.

Injective Graph Homomorphism, Oriented Colouring, Complexity

Campbell, R. , Clarke, N. and MacGillivray, G. (2023) Complexity of Injective Homomorphisms to Small Tournaments, and of Injective Oriented Colourings. Open Journal of Discrete Mathematics, 13, 1-15. doi: 10.4236/ojdm.2023.131001.