{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:48Z","timestamp":1753893828989,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A tree is called a $k$-tree if its maximum degree is at most $k$.\u00a0We prove the following theorem. Let $k \\geq 2$ be an integer, and\u00a0$G$ be a connected bipartite graph with bipartition $(A,B)$\u00a0such that $|A| \\le |B| \\le (k-1)|A|+1$. If $\\sigma_k(G) \\ge |B|$, then $G$ has a spanning $k$-tree,\u00a0where $\\sigma_k(G)$ denotes the minimum degree sum of $k$ independent vertices of $G$.\u00a0Moreover, the condition on $\\sigma_k(G)$ is sharp.\u00a0It was shown by Win (Abh. Math. Sem. Univ. Hamburg, 43, 263\u2013267, 1975) that if a connected graph $H$ satisfies $\\sigma_k(H) \\ge |H|-1$,\u00a0then $H$ has a spanning $k$-tree.\u00a0Thus our theorem shows that the condition becomes much weaker if the graph is bipartite.<\/jats:p>","DOI":"10.37236\/3628","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T19:33:18Z","timestamp":1578684798000},"source":"Crossref","is-referenced-by-count":4,"title":["Spanning $k$-trees of Bipartite Graphs"],"prefix":"10.37236","volume":"22","author":[{"given":"Mikio","family":"Kano","sequence":"first","affiliation":[]},{"given":"Kenta","family":"Ozeki","sequence":"additional","affiliation":[]},{"given":"Kazuhiro","family":"Suzuki","sequence":"additional","affiliation":[]},{"given":"Masao","family":"Tsugaki","sequence":"additional","affiliation":[]},{"given":"Tomoki","family":"Yamashita","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,1,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p13\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p13\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:38:44Z","timestamp":1579239524000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i1p13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1,20]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/3628","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,1,20]]},"article-number":"P1.13"}}