{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:11Z","timestamp":1753893851425,"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>Let $i(r,g)$ denote the infimum of the ratio $\\frac{\\alpha(G)}{|V(G)|}$ over the $r$-regular graphs of girth at least $g$, where $\\alpha(G)$ is the independence number of $G$, and\u00a0 let $i(r,\\infty) := \\lim\\limits_{g \\to \\infty} i(r,g)$. Recently, several new lower bounds of $i(3,\\infty)$ were obtained. In particular, Hoppen and Wormald showed in 2015 that $i(3, \\infty) \\geqslant 0.4375,$ and Cs\u00f3ka improved it to $i(3,\\infty) \\geqslant 0.44533$ in 2016. Bollob\u00e1s proved the upper bound\u00a0 $i(3,\\infty) &lt; \\frac{6}{13}$\u00a0 in 1981, and McKay improved it to $i(3,\\infty) &lt; 0.45537$in 1987. There were no improvements since then. In this paper, we improve the upper bound to $i(3,\\infty) \\leqslant 0.454.$<\/jats:p>","DOI":"10.37236\/7272","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:11:29Z","timestamp":1578640289000},"source":"Crossref","is-referenced-by-count":1,"title":["Cubic Graphs with Small Independence Ratio"],"prefix":"10.37236","volume":"26","author":[{"given":"J\u00f3zsef","family":"Balogh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexandr","family":"Kostochka","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xujun","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2019,3,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i1p43\/7802","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i1p43\/7802","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:15:50Z","timestamp":1579234550000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i1p43"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,22]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/7272","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,3,22]]},"article-number":"P1.43"}}