@article{Hell1995OnHT,
title={On homomorphisms to acyclic local tournaments},
author={Pavol Hell and Huishan Zhou and Xuding Zhu},
journal={Journal of Graph Theory},
year={1995},
volume={20},
pages={467-471}
}

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