{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,6]],"date-time":"2022-04-06T04:03:58Z","timestamp":1649217838977},"reference-count":20,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2012,6]]},"abstract":"<jats:p>Lov\u00e1sz and Plummer conjectured that: for k \u2265 3 there exist constants c<jats:sub>1<\/jats:sub>(k) &gt; 1 and c<jats:sub>2<\/jats:sub>(k) &gt; 0 such that every k-regular elementary graph on 2n vertices, without forbidden edges, contains at least c<jats:sub>2<\/jats:sub>(k)\u22c5c<jats:sub>1<\/jats:sub>(k)<jats:sup>n<\/jats:sup>perfect matchings. Furthermore c<jats:sub>1<\/jats:sub>(k) \u2192 \u221e as k \u2192 \u221e. In this paper, for some Cartesian products of graphs, we obtain a lower bound of their number of perfect matchings which is similar to that of Lov\u00e1sz and Plummer's conjecture. Furthermore, we compute the genus of some Cartesian products of graphs.<\/jats:p>","DOI":"10.1142\/s1793830912500267","type":"journal-article","created":{"date-parts":[[2012,6,19]],"date-time":"2012-06-19T14:55:53Z","timestamp":1340117753000},"page":"1250026","source":"Crossref","is-referenced-by-count":0,"title":["PERFECT MATCHINGS AND GENUS OF SOME CARTESIAN PRODUCTS OF GRAPHS"],"prefix":"10.1142","volume":"04","author":[{"given":"FENGGEN","family":"LIN","sequence":"first","affiliation":[{"name":"College of Mathematics and Computer Science, Fuzhou University, Fujian 350108, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"LIANZHU","family":"ZHANG","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Xiamen University, Fujian 361005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"FULIANG","family":"LU","sequence":"additional","affiliation":[{"name":"School of Science, Linyi University, Shandong 276000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,6,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1006\/jcta.1996.2725"},{"key":"rf2","doi-asserted-by":"crossref","first-page":"#R45","DOI":"10.37236\/1738","volume":"10","author":"Fischer I.","journal-title":"Electron. 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