{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T06:56:44Z","timestamp":1775631404720,"version":"3.50.1"},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"1-2","license":[{"start":{"date-parts":[[2012,2,2]],"date-time":"2012-02-02T00:00:00Z","timestamp":1328140800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2012,3]]},"abstract":"<jats:p>A spanning tree <jats:italic>T<\/jats:italic> of a graph <jats:italic>G<\/jats:italic> is called a <jats:italic>homeomorphically irreducible spanning tree<\/jats:italic> (HIST) if <jats:italic>T<\/jats:italic> does not contain vertices of degree 2. A graph <jats:italic>G<\/jats:italic> is called <jats:italic>locally connected<\/jats:italic> if, for every vertex <jats:italic>v<\/jats:italic> \u2208 <jats:italic>V<\/jats:italic>(<jats:italic>G<\/jats:italic>), the subgraph induced by the neighbourhood of <jats:italic>v<\/jats:italic> is connected. In this paper, we prove that every connected and locally connected graph with more than 3 vertices contains a HIST. Consequently, we confirm the following conjecture due to Archdeacon: every graph that triangulates some surface has a HIST, which was proposed as a question by Albertson, Berman, Hutchinson and Thomassen.<\/jats:p>","DOI":"10.1017\/s0963548311000526","type":"journal-article","created":{"date-parts":[[2012,3,19]],"date-time":"2012-03-19T11:20:59Z","timestamp":1332156059000},"page":"107-111","source":"Crossref","is-referenced-by-count":18,"title":["Homeomorphically Irreducible Spanning Trees in Locally Connected Graphs"],"prefix":"10.1017","volume":"21","author":[{"given":"GUANTAO","family":"CHEN","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"HAN","family":"REN","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"SONGLING","family":"SHAN","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2012,2,2]]},"reference":[{"key":"S0963548311000526_ref7","first-page":"362","volume-title":"Second International Conference on Combinatorial Mathematics, New York 1978","author":"Malkevitch","year":"1979"},{"key":"S0963548311000526_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84628-970-5"},{"key":"S0963548311000526_ref6","volume-title":"The Steiner Tree Problem","author":"Hwang","year":"1992"},{"key":"S0963548311000526_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139087223"},{"key":"S0963548311000526_ref1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190140212"},{"key":"S0963548311000526_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0070403"},{"key":"S0963548311000526_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511662072.011"},{"key":"S0963548311000526_ref4","first-page":"265","volume-title":"Graph Theory, Combinatorics, and Algorithms: Kalamazoo 1992","author":"Davidow","year":"1995"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548311000526","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,25]],"date-time":"2019-04-25T21:25:18Z","timestamp":1556227518000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548311000526\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,2]]},"references-count":8,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2012,3]]}},"alternative-id":["S0963548311000526"],"URL":"https:\/\/doi.org\/10.1017\/s0963548311000526","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,2,2]]}}}