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...

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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
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Online Access:http://dmtcs.episciences.org/9957/pdf
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author Thomas Bellitto
Christopher Duffy
Gary MacGillivray
author_facet Thomas Bellitto
Christopher Duffy
Gary MacGillivray
author_sort Thomas Bellitto
collection DOAJ
description 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.
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institution Kabale University
issn 1365-8050
language English
publishDate 2023-10-01
publisher Discrete Mathematics & Theoretical Computer Science
record_format Article
series Discrete Mathematics & Theoretical Computer Science
spelling doaj-art-65c0f1e5d3ef4ead88f5c8acc30719a22025-08-20T03:42:37ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502023-10-01vol. 25:2Graph Theory10.46298/dmtcs.99579957Homomorphically Full Oriented GraphsThomas BellittoChristopher Duffyhttps://orcid.org/0000-0003-1657-3172Gary MacGillivrayHomomorphically 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.http://dmtcs.episciences.org/9957/pdfcomputer science - discrete mathematicsmathematics - combinatorics05c60, 05c20, 68q17
spellingShingle Thomas Bellitto
Christopher Duffy
Gary MacGillivray
Homomorphically Full Oriented Graphs
Discrete Mathematics & Theoretical Computer Science
computer science - discrete mathematics
mathematics - combinatorics
05c60, 05c20, 68q17
title Homomorphically Full Oriented Graphs
title_full Homomorphically Full Oriented Graphs
title_fullStr Homomorphically Full Oriented Graphs
title_full_unstemmed Homomorphically Full Oriented Graphs
title_short Homomorphically Full Oriented Graphs
title_sort homomorphically full oriented graphs
topic computer science - discrete mathematics
mathematics - combinatorics
05c60, 05c20, 68q17
url http://dmtcs.episciences.org/9957/pdf
work_keys_str_mv AT thomasbellitto homomorphicallyfullorientedgraphs
AT christopherduffy homomorphicallyfullorientedgraphs
AT garymacgillivray homomorphicallyfullorientedgraphs