Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Bastide, Paul, Duron, Julien, Hodor, Jędrzej, Liu, Weichan, Nie, Xiangxiang
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funders: Shandong University, European Commission
Award: G434337789
OpenAlex ID: W7104289660
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