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Swarts, J. (2008) The Complexity of Digraph Homomorphisms: Local Tournaments, Injective Homomorphisms and Polymorphisms. Ph.D. Thesis, University of Victoria, Victoria.

has been cited by the following article:

• 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.