{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:20Z","timestamp":1753893800128,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For a tree $T$, let $V_{2}(T)$ denote the set of vertices of $T$ having degree $2$. Let $G$ be a connected graph. A spanning tree $T$ of $G$ with $V_{2}(T)=\\emptyset $ is called a homeomorphically irreducible spanning tree (or a HIST) of $G$.\r\nWe focus on two relaxations of HISTs as follows:(1) A spanning tree $T$ of $G$ such that the maximum order of components of the subgraph of $T$ induced by $V_{2}(T)$ is bounded.(2) A spanning tree $T$ of $G$ such that $|V_{2}(T)|$ is bounded.A spanning tree satisfying (1) was recently introduced by Lyngsie and Merker, and a spanning tree satisfying (2) is known as a tool for constructing a HIST. In this paper, we define an SP-system, which is a useful concept for finding a spanning tree satisfying (1) or (2) (or both). To demonstrate how the concept works, we characterize forbidden subgraph conditions forcing connected graphs to have such spanning trees.<\/jats:p>","DOI":"10.37236\/11920","type":"journal-article","created":{"date-parts":[[2024,9,20]],"date-time":"2024-09-20T09:33:54Z","timestamp":1726824834000},"source":"Crossref","is-referenced-by-count":0,"title":["Forbidden Subgraphs Restricting Vertices of Degree Two in a Spanning Tree"],"prefix":"10.37236","volume":"31","author":[{"given":"Michitaka","family":"Furuya","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shoichi","family":"Tsuchiya","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2024,9,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i3p31\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i3p31\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,20]],"date-time":"2024-09-20T09:33:54Z","timestamp":1726824834000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i3p31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,13]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,7,12]]}},"URL":"https:\/\/doi.org\/10.37236\/11920","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2024,9,13]]},"article-number":"P3.31"}}