{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T04:51:00Z","timestamp":1697691060935},"reference-count":14,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2005,3,16]],"date-time":"2005-03-16T00:00:00Z","timestamp":1110931200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2005,6]]},"abstract":"Abstract<\/jats:title>The hamiltonian index of a graph G<\/jats:italic> is the smallest integer k<\/jats:italic> such that the k<\/jats:italic>\u2010th iterated line graph of G<\/jats:italic> is hamiltonian. We first show that, with one exceptional case, adding an edge to a graph cannot increase its hamiltonian index. We use this result to prove that neither the contraction of an AG<\/jats:sub><\/jats:italic>(F<\/jats:italic>)\u2010contractible subgraph F<\/jats:italic> of a graph G<\/jats:italic> nor the closure operation performed on G<\/jats:italic> (if G<\/jats:italic> is claw\u2010free) affects the value of the hamiltonian index of a graph G<\/jats:italic>. AMS Subject Classification (2000): 05C45, 05C35. \u00a9 2005 Wiley Periodicals, Inc. J Graph Theory<\/jats:p>","DOI":"10.1002\/jgt.20068","type":"journal-article","created":{"date-parts":[[2005,3,16]],"date-time":"2005-03-16T18:47:04Z","timestamp":1110998824000},"page":"104-115","source":"Crossref","is-referenced-by-count":6,"title":["On stability of the hamiltonian index under contractions and closures"],"prefix":"10.1002","volume":"49","author":[{"given":"Liming","family":"Xiong","sequence":"first","affiliation":[]},{"given":"Zden\u011bk","family":"Ryj\u00e1\u010dek","sequence":"additional","affiliation":[]},{"given":"Hajo","family":"Broersma","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2005,3,16]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0118(200005)34:1<30::AID-JGT4>3.0.CO;2-R"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/s003730050002"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190120105"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1965-051-3"},{"key":"e_1_2_1_7_2","first-page":"115","article-title":"Closure, path\u2010factors and path coverings in claw\u2010free graphs","volume":"50","author":"Ishizuka S.","year":"1998","journal-title":"Ars Combinatoria"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(84)90004-9"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(99)00234-4"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1996.1732"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0118(199910)32:2<109::AID-JGT1>3.0.CO;2-O"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.10103"},{"key":"e_1_2_1_13_2","unstructured":"L.Xiong Circuits in graphs and the hamiltonian index. PhD Thesis University of Twente Enschede The Netherlands 2001 ISBN 9036516196."},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(01)00442-3"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2004.01.018"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.20068","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.20068","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T16:58:19Z","timestamp":1697648299000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.20068"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,3,16]]},"references-count":14,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2005,6]]}},"alternative-id":["10.1002\/jgt.20068"],"URL":"https:\/\/doi.org\/10.1002\/jgt.20068","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,3,16]]}}}