{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T06:40:35Z","timestamp":1698043235921},"reference-count":6,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":6305,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1989,7]]},"abstract":"Abstract<\/jats:title>Suppose that a connected graph G has n vertices and m edges, and each edge is contained in some triangle of G. Bounds are established here on the minimum number tmin<\/jats:sub>(G) of triangles that cover the edges of G.<\/jats:p>We prove that \u2308(n \u2010 1)\/2\u2309 \u2a7d tmin<\/jats:sub>(G) with equality attained only by 3\u2010cactii and by strongly related graphs.<\/jats:p>We obtain sharp upper bounds: if G is not a 4\u2010clique, then.<\/jats:p>magnified image<\/jats:alt-text><\/jats:graphic><\/jats:chem-struct><\/jats:chem-struct-wrap><\/jats:p>The triangle cover number tmin<\/jats:sub>(G) is also bounded above by \u0393(G) = m \u2010 n + c, the cyclomatic number of a graph G of order n with m edges and c connected components. Here we give a combinatorial proof for tmin<\/jats:sub>(G) \u2a7d \u0393(G) and characterize the family of all extremal graphs satisfying equality.<\/jats:p>","DOI":"10.1002\/jgt.3190130312","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T12:26:24Z","timestamp":1180182384000},"page":"369-384","source":"Crossref","is-referenced-by-count":1,"title":["The minimum number of triangles covering the edges of a graph"],"prefix":"10.1002","volume":"13","author":[{"given":"Jen\u00f6","family":"Lehel","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Graphs and hypergraphs","author":"Berge C.","year":"1973"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1966-014-3"},{"key":"e_1_2_1_4_2","unstructured":"T.Gallai personal communication (1987)."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(82)90040-1"},{"key":"e_1_2_1_6_2","volume-title":"Combinatorial Problems and Exercises","author":"Lov\u00e1sz L.","year":"1979"},{"key":"e_1_2_1_7_2","first-page":"436","article-title":"Egy gr\u00e1felm\u00e9leti sz\u00e9ls\u00f6\u00e9rt\u00e9k feladatrol","volume":"48","author":"Tur\u00e1n P.","year":"1941","journal-title":"Mat. Fiz. Lapok"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190130312","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190130312","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T13:28:20Z","timestamp":1697981300000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190130312"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,7]]},"references-count":6,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1989,7]]}},"alternative-id":["10.1002\/jgt.3190130312"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190130312","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,7]]}}}