{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:49Z","timestamp":1753893829563,"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>The goal of this paper is to find vertex disjoint even cycles in graphs.  For this purpose, define a $\\theta$-graph to be a pair of vertices $u, v$ with three internally disjoint paths joining $u$ to $v$.  Given an independence number $\\alpha$ and a fixed integer $k$, the results contained in this paper provide sharp bounds on the order $f(k, \\alpha)$ of a graph with independence number $\\alpha(G) \\leq \\alpha$ which contains no $k$ disjoint $\\theta$-graphs.  Since every $\\theta$-graph contains an even cycle, these results provide $k$ disjoint even cycles in graphs of order at least $f(k, \\alpha) + 1$.  We also discuss the relationship between this problem and a generalized ramsey problem involving sets of graphs.<\/jats:p>","DOI":"10.37236\/637","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:43:48Z","timestamp":1578714228000},"source":"Crossref","is-referenced-by-count":0,"title":["Independence Number and Disjoint Theta Graphs"],"prefix":"10.37236","volume":"18","author":[{"given":"Shinya","family":"Fujita","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Colton","family":"Magnant","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,7,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p150\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p150\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:07:51Z","timestamp":1579302471000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p150"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,7,22]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/637","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,7,22]]},"article-number":"P150"}}