On homomorphisms to acyclic local tournaments

  title={On homomorphisms to acyclic local tournaments},
  author={Pavol Hell and Huishan Zhou and Xuding Zhu},
  journal={Journal of Graph Theory},
A homomorphism of a digraph to another digraph is an edgepreserving vertex mapping. A local tournament is a digraph in which the inset as well as the outset of each vertex induces a tournament. Thus acyclic local tournaments generalize both directed paths and transitive tournaments. In both these cases there is a simple characterization of homomorphic preimages. Namely, if H is a directed path, or a transitive tournament, then G admits a homomorphism to H if and only if each oriented path which… CONTINUE READING

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