{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T13:42:22Z","timestamp":1698068542866},"reference-count":16,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":6152,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1989,12]]},"abstract":"Abstract<\/jats:title>This paper deals with the problem of characterizing the pairs of vertices x,y<\/jats:italic> in a connected graph G<\/jats:italic> such that G<\/jats:italic>3<\/jats:sup> \u2010 {x,y<\/jats:italic>} is hamiltonian, where G<\/jats:italic>3<\/jats:sup> is the cube of G.<\/jats:italic> It is known that the cube G<\/jats:italic>3<\/jats:sup> is 2\u2010hamiltonian if G<\/jats:italic> is 2\u2010connected. In this paper, we first prove the stronger result that G<\/jats:italic>3<\/jats:sup> \u2010 {x,y<\/jats:italic>} is hamiltonian if either x<\/jats:italic> or y<\/jats:italic> is not a cut\u2010vertex of G<\/jats:italic>, and then proceed to characterize those cut\u2010vertices x<\/jats:italic> and y<\/jats:italic> of G<\/jats:italic> such that G<\/jats:italic>3<\/jats:sup> \u2010{x,y<\/jats:italic>} is hamiltonian. As a simple consequence of these, we obtain Schaar's characterization of a connected graph G<\/jats:italic> such that G<\/jats:italic>3<\/jats:sup> is 2\u2010hamiltonian.<\/jats:p>","DOI":"10.1002\/jgt.3190130609","type":"journal-article","created":{"date-parts":[[2007,6,8]],"date-time":"2007-06-08T22:52:35Z","timestamp":1181343155000},"page":"737-747","source":"Crossref","is-referenced-by-count":5,"title":["The 2\u2010hamiltonian cubes of graphs"],"prefix":"10.1002","volume":"13","author":[{"given":"K. M.","family":"Koh","sequence":"first","affiliation":[]},{"given":"K. L.","family":"Teo","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Graphs and Digraphs","author":"Behzad M.","year":"1979"},{"key":"e_1_2_1_3_2","first-page":"63","article-title":"The powers of a connected graph are highly hamiltonian","volume":"75","author":"Bhat V. N.","year":"1971","journal-title":"J. Res. National Bureau Standard"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"issue":"1","key":"e_1_2_1_5_2","first-page":"47","article-title":"The cube of every connected graph is 1\u2010hamiltonian","volume":"73","author":"Chartrand G.","year":"1969","journal-title":"J. Res. National Bureau Standard"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(70)80069-2"},{"issue":"1","key":"e_1_2_1_7_2","first-page":"1","article-title":"Some hamiltonian results in powers of graphs","volume":"77","author":"Hobbs A. M.","year":"1973","journal-title":"J. Res. National Bureau Standard"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(79)90040-6"},{"key":"e_1_2_1_9_2","first-page":"109","article-title":"A note on the powers of 2\u2010connected graphs","volume":"27","author":"Kapoor S. F.","year":"1972","journal-title":"Elem. Math."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1968-037-0"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(73)90058-0"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(84)90106-7"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190120109"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1002\/mana.19710510113"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1002\/mana.19750660114"},{"key":"e_1_2_1_16_2","first-page":"959","article-title":"On 3\u2010hamiltonian cubes of connected graphs. Combinatorics, (Proceedings of the 5th Hungarian Colloqium in Keszthely, 1976), Vol. II","volume":"18","author":"Schaar G.","year":"1978","journal-title":"Colloq. Math. Soc. J\u00e1nos Bolyai"},{"key":"e_1_2_1_17_2","unstructured":"M.Sekanina On an ordering of the set of vertices of a connected graph. Publication of the Faculty of Science University of Brno. Tchecoslovaquie No. 412 (1960)137\u2013141."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190130609","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190130609","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T02:57:37Z","timestamp":1697943457000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190130609"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,12]]},"references-count":16,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1989,12]]}},"alternative-id":["10.1002\/jgt.3190130609"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190130609","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,12]]}}}