{"ID":2835358,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.22912","arxiv_id":"2511.22912","title":"Spanning Trees with a Small Vertex Cover: the Complexity on Specific Graph Classes","abstract":"In the context of algorithm theory, various studies have been conducted on spanning trees with desirable properties. In this paper, we consider the \\textsc{Minimum Cover Spanning Tree} problem (MCST for short). Given a graph $G$ and a positive integer $k$, the problem determines whether $G$ has a spanning tree with a vertex cover of size at most $k$. We reveal the equivalence between \\mcst\\ and the \\textsc{Dominating Set} problem when $G$ is of diameter at most~$2$ or $P_5$-free. This provides the intractability for these graphs and the tractability for several subclasses of $P_5$-free graphs. We also show that \\mcst\\ is NP-complete for bipartite planar graphs of maximum degree~$4$ and unit disk graphs. These hardness results resolve open questions posed in prior research. Finally, we present an FPT algorithm for {\\mcst} parameterized by clique-width and a linear-time algorithm for interval graphs.","short_abstract":"In the context of algorithm theory, various studies have been conducted on spanning trees with desirable properties. In this paper, we consider the \\textsc{Minimum Cover Spanning Tree} problem (MCST for short). Given a graph $G$ and a positive integer $k$, the problem determines whether $G$ has a spanning tree with a v...","url_abs":"https://arxiv.org/abs/2511.22912","url_pdf":"https://arxiv.org/pdf/2511.22912v1","authors":"[\"Toranosuke Kokai\",\"Akira Suzuki\",\"Takahiro Suzuki\",\"Yuma Tamura\",\"Xiao Zhou\"]","published":"2025-11-28T06:34:37Z","proceeding":"cs.DS","tasks":"[\"cs.DS\"]","methods":"[]","has_code":false}