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<p>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 (<i>T</i>,&#xa0;<i>t</i>), 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 (<i>N</i>,&#xa0;<i>t</i>).</p>

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Representing distance-hereditary graphs with multi-rooted trees

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  • 发表日期：

    2025年9月27日

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  • Guillaume E. Scholz

摘要

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).