{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:24Z","timestamp":1753893804160,"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>For integers $k,n$ with $1 \\le k \\le n\/2$, let $f(k,n)$ be the smallest integer $t$ such that every $t$-connected $n$-vertex graph has a spanning bipartite $k$-connected subgraph. A conjecture of Thomassen asserts that $f(k,n)$ is upper bounded by some function of $k$. The best upper bound for $f(k,n)$ is by Delcourt and Ferber who proved that $f(k,n) \\le 10^{10}k^3 \\log n$. Here it is proved that $f(k,n) \\le 22k^2 \\log n$. For larger $k$, stronger bounds hold. In the linear regime, it is proved that for any $0 &lt; c &lt; \\frac{1}{2}$ and all sufficiently large $n$, $f(\\lfloor cn \\rfloor, n) \\le 30\\sqrt{c}n$. In the polynomial regime, it is proved that for any $\\frac{1}{3} \\le \\alpha &lt; 1$ and all sufficiently large $n$, $f(\\lfloor n^\\alpha \\rfloor ,n) \\le 9n^{(1+\\alpha)\/2}$.<\/jats:p>","DOI":"10.37236\/12084","type":"journal-article","created":{"date-parts":[[2024,3,21]],"date-time":"2024-03-21T16:23:15Z","timestamp":1711038195000},"source":"Crossref","is-referenced-by-count":0,"title":["Highly Connected Graphs Have Highly Connected Spanning Bipartite Subgraphs"],"prefix":"10.37236","volume":"31","author":[{"given":"Raphael","family":"Yuster","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2024,3,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i1p67\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i1p67\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,21]],"date-time":"2024-03-21T16:23:15Z","timestamp":1711038195000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i1p67"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,22]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,1,12]]}},"URL":"https:\/\/doi.org\/10.37236\/12084","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2024,3,22]]},"article-number":"P1.67"}}