Homomorphically Full Oriented Graphs

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 orientat...

Full description

Saved in:
Bibliographic Details
Main Authors: Thomas Bellitto, Christopher Duffy, Gary MacGillivray
Format: Article
Language:English
Published: Discrete Mathematics & Theoretical Computer Science 2023-10-01
Series:Discrete Mathematics & Theoretical Computer Science
Subjects:
Online Access:http://dmtcs.episciences.org/9957/pdf
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1365-8050