{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:11Z","timestamp":1753893791914,"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 2-factor-plus-triangles graph is the union of two $2$-regular graphs $G_1$ and $G_2$ with the same vertices, such that $G_2$ consists of disjoint triangles.  Let ${\\cal G}$ be the family of such graphs.  These include the famous \"cycle-plus-triangles\" graphs shown to be $3$-choosable by Fleischner and Stiebitz.  The independence ratio of a graph in ${\\cal G}$ may be less than $1\/3$; but achieving the minimum value $1\/4$ requires each component to be isomorphic to the 12-vertex \"Du\u2013Ngo\" graph.  Nevertheless, ${\\cal G}$ contains infinitely many connected graphs with independence ratio less than $4\/15$.  For each odd $g$ there are infinitely many connected graphs in ${\\cal G}$ such that $G_1$ has girth $g$ and the independence ratio of $G$ is less than $1\/3$.  Also, when $12$ divides $n$ (and $n\\ne12$) there is an $n$-vertex graph in ${\\cal G}$ such that $G_1$ has girth $n\/2$ and $G$ is not $3$-colorable.  Finally, unions of two graphs whose components have at most $s$ vertices are $s$-choosable.<\/jats:p>","DOI":"10.37236\/116","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:35:45Z","timestamp":1578717345000},"source":"Crossref","is-referenced-by-count":0,"title":["Independence Number of 2-Factor-Plus-Triangles Graphs"],"prefix":"10.37236","volume":"16","author":[{"given":"Jennifer","family":"Vandenbussche","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Douglas B.","family":"West","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2009,2,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r27\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r27\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T03:12:29Z","timestamp":1579317149000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,2,27]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/116","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,2,27]]},"article-number":"R27"}}