Homomorphically Full Oriented Graphs
Discrete Mathematics
2024-02-14 v3 Combinatorics
Abstract
Homomorphically full graphs are those for which every homomorphic image is isomorphic to a subgraph. We extend the definition of homomorphically full to oriented graphs in two different ways. For the first of these, we show that homomorphically full oriented graphs arise as quasi-transitive orientations of homomorphically full graphs. This in turn yields an efficient recognition and construction algorithms for these homomorphically full oriented graphs. For the second one, we show that the related recognition problem is GI-hard, and that the problem of deciding if a graph admits a homomorphically full orientation is NP-complete. In doing so we show the problem of deciding if two given oriented cliques are isomorphic is GI-complete.
Keywords
Cite
@article{arxiv.2208.10727,
title = {Homomorphically Full Oriented Graphs},
author = {Thomas Bellitto and Christopher Duffy and Gary MacGillivray},
journal= {arXiv preprint arXiv:2208.10727},
year = {2024}
}