Homomorphically Full Oriented Graphs
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866917588050640896 |
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| author | Bellitto, Thomas Duffy, Christopher MacGillivray, Gary |
| author_facet | Bellitto, Thomas Duffy, Christopher MacGillivray, Gary |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_10727 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Homomorphically Full Oriented Graphs Bellitto, Thomas Duffy, Christopher MacGillivray, Gary Discrete Mathematics Combinatorics 05C60, 05C20, 68Q17 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. |
| title | Homomorphically Full Oriented Graphs |
| topic | Discrete Mathematics Combinatorics 05C60, 05C20, 68Q17 |
| url | https://arxiv.org/abs/2208.10727 |