Representing distance-hereditary graphs with multi-rooted trees
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917919855738880 |
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| author | Scholz, Guillaume E. |
| author_facet | Scholz, Guillaume E. |
| contents | Arboreal networks are a generalization of rooted trees, defined by keeping the tree-like structure, but dropping the requirement for a single root. Just as the class of cographs is precisely the class of undirected graphs that can be explained by a labelled rooted tree (T,t), we show that the class of distance-hereditary graphs is precisely the class of undirected graphs that can be explained by a labelled arboreal network (N,t). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08251 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Representing distance-hereditary graphs with multi-rooted trees Scholz, Guillaume E. Combinatorics 05C05, 05C20, 05C62 Arboreal networks are a generalization of rooted trees, defined by keeping the tree-like structure, but dropping the requirement for a single root. Just as the class of cographs is precisely the class of undirected graphs that can be explained by a labelled rooted tree (T,t), we show that the class of distance-hereditary graphs is precisely the class of undirected graphs that can be explained by a labelled arboreal network (N,t). |
| title | Representing distance-hereditary graphs with multi-rooted trees |
| topic | Combinatorics 05C05, 05C20, 05C62 |
| url | https://arxiv.org/abs/2502.08251 |