{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T09:43:57Z","timestamp":1698227037821},"reference-count":11,"publisher":"Wiley","issue":"7","license":[{"start":{"date-parts":[[2006,10,6]],"date-time":"2006-10-06T00:00:00Z","timestamp":1160092800000},"content-version":"vor","delay-in-days":4357,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1994,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For several years, the study of neighborhood unions of graphs has given rise to important structural consequences of graphs. In particular, neighborhood conditions that give rise to hamiltonian cycles have been considered in depth. In this paper we generalize these approaches to give a bound on the smallest number of cycles in <jats:italic>G<\/jats:italic> containing all the vertices of <jats:italic>G<\/jats:italic>.<\/jats:p><jats:p>We show that if for all <jats:italic>x<\/jats:italic>, <jats:italic>y<\/jats:italic> \u2245 <jats:italic>V<\/jats:italic>(<jats:italic>G<\/jats:italic>), |<jats:italic>N<\/jats:italic>(<jats:italic>x<\/jats:italic>) \u2229 <jats:italic>N<\/jats:italic>(<jats:italic>y<\/jats:italic>)| \u2267 2<jats:italic>n<\/jats:italic>\/5 + 1, then <jats:italic>V<\/jats:italic>(<jats:italic>G<\/jats:italic>) is coverable by at most two cycles. Several related results and extensions to <jats:italic>t<\/jats:italic> cycles are also given.<\/jats:p>","DOI":"10.1002\/jgt.3190180703","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T16:20:18Z","timestamp":1181233218000},"page":"663-672","source":"Crossref","is-referenced-by-count":1,"title":["Neighborhood unions and the cycle cover number of a graph"],"prefix":"10.1002","volume":"18","author":[{"given":"Guantao","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ronald J.","family":"Gould","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael S.","family":"Jacobson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Richard H.","family":"Schelp","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,6]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"J.Bondy Longest paths and cycles in graphs of high degree.CORR80\u201316 Department of Combinatorics Waterloo."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190150106"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-2.1.69"},{"key":"e_1_2_1_5_2","unstructured":"H.Enomoto A.Kaneko M.Kouider andZs.Tuza Degree sums and covering cycles. Manuscript (1990)."},{"key":"e_1_2_1_6_2","unstructured":"H.Enomoto A.Kaneko andZs.Tuza Graphs of ordernwith minimum degree at leastn\/3. University of Tokyo Technical Report 87\u201320."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(92)90132-Y"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02651085"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190110413"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(89)90060-9"},{"key":"e_1_2_1_11_2","unstructured":"Y.Manoussakis Covering by cycles the vertices of 3\u2010connected graph. Manuscript (1988)."},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(83)90165-6"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190180703","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190180703","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T17:48:10Z","timestamp":1698169690000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190180703"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,11]]},"references-count":11,"journal-issue":{"issue":"7","published-print":{"date-parts":[[1994,11]]}},"alternative-id":["10.1002\/jgt.3190180703"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190180703","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,11]]}}}