{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:14:16Z","timestamp":1758824056567},"reference-count":6,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2006,10,6]],"date-time":"2006-10-06T00:00:00Z","timestamp":1160092800000},"content-version":"vor","delay-in-days":4449,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1994,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We construct 3\u2010regular (cubic) graphs <jats:italic>G<\/jats:italic> that have a dominating cycle <jats:italic>C<\/jats:italic> such that no other cycle <jats:italic>C<\/jats:italic><jats:sub>1<\/jats:sub> of <jats:italic>G<\/jats:italic> satisfies <jats:italic>V(C)<\/jats:italic> \u2286 <jats:italic>V<\/jats:italic>(<jats:italic>C<\/jats:italic><jats:sub>1<\/jats:sub>). By a similar construction we obtain loopless 4\u2010regular graphs having precisely one hamiltonian cycle. The basis for these constructions are considerations on the uniqueness of a cycle decomposition compatible with a given eulerian trail in some eulerian graph.<\/jats:p>","DOI":"10.1002\/jgt.3190180503","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T18:17:35Z","timestamp":1181240255000},"page":"449-459","source":"Crossref","is-referenced-by-count":16,"title":["Uniqueness of maximal dominating cycles in 3\u2010regular graphs and of hamiltonian cycles in 4\u2010regular graphs"],"prefix":"10.1002","volume":"18","author":[{"given":"Herbert","family":"Fleischner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,6]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Selected Topics in Graph Theory","author":"Beineke L. W.","year":"1978"},{"key":"e_1_2_1_3_2","first-page":"233","volume-title":"Progress in Graph Theory","author":"Fleischner H.","year":"1984"},{"key":"e_1_2_1_4_2","first-page":"8","article-title":"Some blood, sweat, but no tears in eulerian graph theory","volume":"63","author":"Fleischner H.","year":"1988","journal-title":"Congres. Numer."},{"key":"e_1_2_1_5_2","article-title":"Eulerian graphs and related topics, Part 1, Vol. 1","volume":"45","author":"Fleischner H.","year":"1990","journal-title":"Ann. Discrete Math."},{"key":"e_1_2_1_6_2","article-title":"Eulerian graphs and related topics, Part 1, Vol. 2","volume":"50","author":"Fleischner H.","year":"1991","journal-title":"Ann. Discrete Math."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70511-9"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190180503","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190180503","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T21:47:38Z","timestamp":1698184058000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190180503"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,8]]},"references-count":6,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1994,8]]}},"alternative-id":["10.1002\/jgt.3190180503"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190180503","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,8]]}}}