{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T19:33:42Z","timestamp":1766086422344},"reference-count":6,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":4028,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1995,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A cycle <jats:italic>C<\/jats:italic> in a graph <jats:italic>G<\/jats:italic> is a <jats:italic>Hamilton cycle<\/jats:italic> if <jats:italic>C<\/jats:italic> contains every vertex of <jats:italic>G<\/jats:italic>. Similarly, a path <jats:italic>P<\/jats:italic> in <jats:italic>G<\/jats:italic> is a <jats:italic>Hamilton path<\/jats:italic> if <jats:italic>P<\/jats:italic> contains every vertex of <jats:italic>G<\/jats:italic>. We say that <jats:italic>G<\/jats:italic> is <jats:italic>Hamilton<\/jats:italic>\u2010<jats:italic>connected<\/jats:italic> if for any pair of vertices, <jats:italic>u<\/jats:italic> and <jats:italic>v<\/jats:italic> of <jats:italic>G<\/jats:italic>, There exists a Hamilton path from <jats:italic>u<\/jats:italic> to <jats:italic>v<\/jats:italic>. If <jats:italic>G<\/jats:italic> is a bipartite graph with bipartition sets of equal size, and there is a Hamilton path from any vertex in one bipartition set to any vertex in the other, The n <jats:italic>G<\/jats:italic> is said to be <jats:italic>Hamilton<\/jats:italic>\u2010<jats:italic>laceable<\/jats:italic>. We present a proof showing that the <jats:italic>n<\/jats:italic>\u2010dimensional <jats:italic>k<\/jats:italic>\u2010ary butterfly graph, denoted BF(k, <jats:italic>n<\/jats:italic>), contains a Hamilton cycle. Then, we use this result in proving the stronger result that <jats:italic>BF<\/jats:italic>(k, <jats:italic>n<\/jats:italic>) is Hamilton\u2010laceable when <jats:italic>n<\/jats:italic> is even and Hamilton\u2010connected for odd values of <jats:italic>n<\/jats:italic>.<\/jats:p>","DOI":"10.1002\/net.3230260304","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T20:21:35Z","timestamp":1179001295000},"page":"145-150","source":"Crossref","is-referenced-by-count":26,"title":["Hamilton cycles and paths in butterfly graphs"],"prefix":"10.1002","volume":"26","author":[{"given":"Stephen A.","family":"Wong","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1137\/0219037"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(94)00087-5"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"e_1_2_1_5_2","article-title":"Hamiltonian cycles and paths in Cayley graphs and digraphs\u2010A survey","author":"Curran S. J.","journal-title":"Discr. Math."},{"key":"e_1_2_1_6_2","volume-title":"Introduction to Parallel Algorithms and Architecture: Arrays, Trees, Hypercubes","author":"Leighton F. T.","year":"1992"},{"key":"e_1_2_1_7_2","volume-title":"Problem 11. Combinatorial Structures and Their Applications","author":"Lov\u00b4sz L.","year":"1970"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230260304","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230260304","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T23:42:16Z","timestamp":1698277336000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230260304"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,10]]},"references-count":6,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1995,10]]}},"alternative-id":["10.1002\/net.3230260304"],"URL":"https:\/\/doi.org\/10.1002\/net.3230260304","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,10]]}}}