{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:38:26Z","timestamp":1753889906936,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2019,8,27]],"date-time":"2019-08-27T00:00:00Z","timestamp":1566864000000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,8,27]],"date-time":"2019-08-27T00:00:00Z","timestamp":1566864000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,8,27]],"date-time":"2019-08-27T00:00:00Z","timestamp":1566864000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p xml:lang=\"en\">Let H =&amp;lt; V, S &amp;gt; be a hypergraph, where V is a set of vertices and S is a set of not necessarily disjoint clusters Si \u2286 V. The Clustered Spanning Tree problem is to find a spanning tree of G which satisfies that each cluster induces a subtree, when it exists. We provide an efficient and unique algorithm which finds a feasible solution tree for H when it exists, or states that no feasible solution exists. The paper also uses special structures of the intersection graph of H to construct a feasible solution more efficiently. For cases when the hypergraph does not have a feasible solution tree, we consider adding vertices to exactly one cluster in order to gain feasibility. We characterize when such addition can gain feasibility, find the appropriate cluster and a possible set of vertices to be added.<\/jats:p>","DOI":"10.23638\/dmtcs-21-1-15","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:54:08Z","timestamp":1743699248000},"source":"Crossref","is-referenced-by-count":0,"title":["Clustered Spanning Tree - Conditions for Feasibility"],"prefix":"10.23638","volume":"vol. 21 no. 1, ICGT 2018","author":[{"given":"Nili","family":"Guttmann-Beck","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zeev","family":"Sorek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michal","family":"Stern","sequence":"additional","affiliation":[{"name":"Caesarea Rothschild Institute and Department of Computer Science"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2019,8,27]]},"container-title":["Discrete Mathematics &amp; Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/hal.science\/hal-01887552v4\/document","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/hal.science\/hal-01887552v4\/document","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:54:08Z","timestamp":1743699248000},"score":1,"resource":{"primary":{"URL":"http:\/\/dmtcs.episciences.org\/4906"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,27]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/dmtcs-21-1-15","relation":{"has-preprint":[{"id-type":"uri","id":"https:\/\/hal.science\/hal-01887552v3","asserted-by":"subject"},{"id-type":"uri","id":"https:\/\/hal.science\/hal-01887552v2","asserted-by":"subject"},{"id-type":"uri","id":"https:\/\/hal.science\/hal-01887552v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"uri","id":"https:\/\/hal.science\/hal-01887552v4","asserted-by":"subject"}]},"ISSN":["1365-8050"],"issn-type":[{"type":"electronic","value":"1365-8050"}],"subject":[],"published":{"date-parts":[[2019,8,27]]},"article-number":"4906"}}