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arXiv · 2502.08251

Representing distance-hereditary graphs with multi-rooted trees

Guillaume E. Scholz
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Abstract

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).

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Guillaume E. Scholz. 2025-02-12. Representing distance-hereditary graphs with multi-rooted trees. https://arxiv.org/abs/2502.08251

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