{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:38:32Z","timestamp":1740155912333,"version":"3.37.3"},"reference-count":6,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771172"],"award-info":[{"award-number":["11771172"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2019,8]]},"abstract":"<jats:p> A [Formula: see text]-tree is a tree with maximum degree at most [Formula: see text]. For a graph [Formula: see text] and [Formula: see text] with [Formula: see text], let [Formula: see text] be the cardinality of a maximum independent set containing [Formula: see text] and [Formula: see text]. For a graph [Formula: see text] and [Formula: see text], the local connectivity [Formula: see text] is defined to be the maximum number of internally disjoint paths connecting [Formula: see text] and [Formula: see text] in [Formula: see text]. In this paper, we prove the following theorem and show the condition is sharp. Let [Formula: see text], [Formula: see text] and [Formula: see text] be integers with [Formula: see text], [Formula: see text] and [Formula: see text]. For any two nonadjacent vertices [Formula: see text] and [Formula: see text] of [Formula: see text], we have [Formula: see text] and [Formula: see text]. Then for any [Formula: see text] distinct vertices of [Formula: see text], [Formula: see text] has a spanning [Formula: see text]-tree such that each of [Formula: see text] specified vertices has degree at most [Formula: see text]. This theorem implies H. Matsuda and H. Matsumura\u2019s result in [on a [Formula: see text]-tree containing specified cleares in a graph, Graphs Combin. 22 (2006) 371\u2013381] and V. Neumann-Lara and E. Rivera-Campo\u2019s result in [Spanning trees with bounded degrees, Combinatorica 11 (1991) 55\u201361]. <\/jats:p>","DOI":"10.1142\/s1793830919500435","type":"journal-article","created":{"date-parts":[[2019,6,28]],"date-time":"2019-06-28T04:08:37Z","timestamp":1561694917000},"page":"1950043","source":"Crossref","is-referenced-by-count":0,"title":["Spanning k-tree with specified vertices"],"prefix":"10.1142","volume":"11","author":[{"given":"Feifei","family":"Song","sequence":"first","affiliation":[{"name":"Department of Information &amp; Computational Science, He\u2019nan Agricultural University, Zhengzhou 450002, P. R. China"}]},{"given":"Jianjie","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Information &amp; Computational Science, He\u2019nan Agricultural University, Zhengzhou 450002, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2019,9,16]]},"reference":[{"key":"S1793830919500435BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(76)90078-9"},{"key":"S1793830919500435BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(72)90079-9"},{"key":"S1793830919500435BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-011-1021-6"},{"key":"S1793830919500435BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-013-1314-z"},{"key":"S1793830919500435BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-006-0660-5"},{"key":"S1793830919500435BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/BF01375473"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830919500435","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,22]],"date-time":"2019-09-22T17:47:45Z","timestamp":1569174465000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830919500435"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8]]},"references-count":6,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2019,8]]}},"alternative-id":["10.1142\/S1793830919500435"],"URL":"https:\/\/doi.org\/10.1142\/s1793830919500435","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2019,8]]}}}