{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T11:04:57Z","timestamp":1769166297772,"version":"3.49.0"},"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>Vizing conjectured in 1963 that $\\gamma(G \\Box H) \\geq \\gamma(G)\\gamma(H)$ for any graphs $G$ and $H$. A graph $G$ is said to satisfy Vizing's conjecture if the conjectured inequality holds for $G$ and any graph $H$.\u00a0 Vizing's conjecture has been proved for $\\gamma(G) \\le 3$, and it is known to hold for other classes of graphs. Clark and Suen in 2000 showed that $\\gamma(G \\Box H) \\geq \\frac{1}{2}\\gamma(G)\\gamma(H)$ for any graphs $G$ and $H$.\u00a0\u00a0 We give a slight improvement of this inequality by tightening their arguments. <\/jats:p>","DOI":"10.37236\/15","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:34:12Z","timestamp":1578713652000},"source":"Crossref","is-referenced-by-count":11,"title":["An Improved Inequality Related to Vizing's Conjecture"],"prefix":"10.37236","volume":"19","author":[{"given":"Stephen","family":"Suen","sequence":"first","affiliation":[]},{"given":"Jennifer","family":"Tarr","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2012,1,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i1p8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i1p8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:57:32Z","timestamp":1579301852000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i1p8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1,6]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2012,2,15]]}},"URL":"https:\/\/doi.org\/10.37236\/15","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,1,6]]},"article-number":"P8"}}