{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T11:52:52Z","timestamp":1772797972002,"version":"3.50.1"},"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>We estimate the minimum number of vertices of a cubic graph\u00a0with given oddness and cyclic connectivity. We prove that a\u00a0bridgeless cubic graph $G$ with oddness $\\omega(G)$ other than\u00a0the Petersen graph has at least $5.41\\, \\omega(G)$ vertices,\u00a0and for each integer $k$ with $2\\le k\\le 6$ we construct an\u00a0infinite family of cubic graphs with cyclic connectivity $k$\u00a0and small oddness ratio $|V(G)|\/\\omega(G)$. In particular, for\u00a0cyclic connectivity $2$, $4$, $5$, and $6$ we improve the upper\u00a0bounds on the oddness ratio of snarks to $7.5$, $13$, $25$, and\u00a0$99$ from the known values $9$, $15$, $76$, and $118$,\u00a0respectively. In addition, we construct a cyclically\u00a0$4$-connected snark of girth $5$ with oddness $4$ on $44$\u00a0vertices, improving the best previous value of $46$.\u00a0Corrigendum added March 19, 2018.<\/jats:p>","DOI":"10.37236\/3969","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T19:31:35Z","timestamp":1578684695000},"source":"Crossref","is-referenced-by-count":8,"title":["Small Snarks with Large Oddness"],"prefix":"10.37236","volume":"22","author":[{"given":"Robert","family":"Luko\u0165ka","sequence":"first","affiliation":[]},{"given":"Edita","family":"M\u00e1\u010dajov\u00e1","sequence":"additional","affiliation":[]},{"given":"J\u00e1n","family":"Maz\u00e1k","sequence":"additional","affiliation":[]},{"given":"Martin","family":"\u0160koviera","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,2,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p51\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p51\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:25:18Z","timestamp":1579238718000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i1p51"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/3969","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,25]]},"article-number":"P1.51"}}