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arXiv · 2511.03524

Covering graphs by isometric trees

Paul Bastide·Julien Duron·Jędrzej Hodor·Weichan Liu·Xiangxiang Nie
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Abstract

A connected subgraph of a graph is isometric if it preserves distances. Recently, graphs admitting a vertex or edge covering by a small number of isometric paths have been studied. In this paper, we consider the analogous problem for isometric trees, focusing on the treewidth of graphs admitting a vertex or edge covering by a small number of such trees. Baste, De Meyer, Giocanti, Objois, and Picavet showed that for coverings by two isometric trees, the treewidth is bounded. We show that already for three isometric trees, the treewidth can be linear in the number of vertices. On the positive side, we show that for graphs of bounded degree coverable by a small number of isometric trees, the treewidth is sublinear in the number of vertices.

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Paul Bastide, Julien Duron, Jędrzej Hodor, Weichan Liu, Xiangxiang Nie. 2026-09-18. Covering graphs by isometric trees. https://arxiv.org/abs/2511.03524

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