{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,8]],"date-time":"2023-11-08T17:02:29Z","timestamp":1699462949469},"reference-count":8,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,6]],"date-time":"2006-11-06T00:00:00Z","timestamp":1162771200000},"content-version":"vor","delay-in-days":6094,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1990,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>M<\/jats:italic> be a matching in a graph <jats:italic>G<\/jats:italic> such that <jats:italic>d<\/jats:italic>(x) + <jats:italic>d<\/jats:italic>(y) \u2265 |<jats:italic>G<\/jats:italic>| for all pairs of independent vertices x and y of G that are incident with <jats:italic>M.<\/jats:italic> We determine a necessary and sufficient condition for <jats:italic>M<\/jats:italic> to be contained in a cycle of <jats:italic>G.<\/jats:italic> This extends results of H\u00e4ggkvist and Berman, and implies that if <jats:italic>M<\/jats:italic> is a 1\u2010factor of <jats:italic>G<\/jats:italic> and |<jats:italic>G<\/jats:italic>| \uf8fd 0 (mod 4), then <jats:italic>M<\/jats:italic> is contained in a Hamilton cycle of <jats:italic>G<\/jats:italic>. We use our results to deduce that an eulerian graph of minimum degree 2k contains k pairwise compatible Euler tours.<\/jats:p>","DOI":"10.1002\/jgt.3190140114","type":"journal-article","created":{"date-parts":[[2007,6,8]],"date-time":"2007-06-08T11:24:31Z","timestamp":1181301871000},"page":"127-138","source":"Crossref","is-referenced-by-count":10,"title":["Cycles containing matchings and pairwise compatible euler tours"],"prefix":"10.1002","volume":"14","author":[{"given":"Bill","family":"Jackson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicholas C.","family":"Wormald","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,6]]},"reference":[{"key":"e_1_2_1_2_2","article-title":"Graphs containing every matching in a cycle","author":"Benhocine A.","journal-title":"Discrete Math."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(83)90264-9"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","unstructured":"H.Fleischner A. J. W.Hilton andB.Jackson On the maximum number of pairwise compatible Euler cycles.J. Graph Theory 51\u201363.","DOI":"10.1002\/jgt.3190140106"},{"key":"e_1_2_1_5_2","first-page":"219","volume-title":"Graph Theory and Related Topics","author":"H\u00e4ggkvist R.","year":"1979"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(82)90078-4"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(87)90125-7"},{"key":"e_1_2_1_8_2","first-page":"82","article-title":"Problem 5","volume":"4","author":"Lovasz L.","year":"1974","journal-title":"Period Math. Hungar."},{"key":"e_1_2_1_9_2","first-page":"547","article-title":"Hamiltonian cycles through matchings","volume":"22","author":"Wojda A. P.","year":"1988","journal-title":"Demonstratio Math."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190140114","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190140114","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T18:54:24Z","timestamp":1698000864000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190140114"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,3]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1990,3]]}},"alternative-id":["10.1002\/jgt.3190140114"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190140114","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,3]]}}}