{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,24]],"date-time":"2023-11-24T15:14:34Z","timestamp":1700838874472},"reference-count":18,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,6]],"date-time":"2006-10-06T00:00:00Z","timestamp":1160092800000},"content-version":"vor","delay-in-days":4023,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1995,10]]},"abstract":"Abstract<\/jats:title>Let G<\/jats:italic> be a simple undirected graph of order n<\/jats:italic>. For an independent set S<\/jats:italic> \u2282 V<\/jats:italic>(G<\/jats:italic>) of k<\/jats:italic> vertices, we define the k<\/jats:italic> neighborhood intersections S<\/jats:italic>i<\/jats:italic><\/jats:sub> = {v<\/jats:italic> \u03f5 V<\/jats:italic>(G<\/jats:italic>)&&num;92;S<\/jats:italic>|N<\/jats:italic>(v<\/jats:italic>) \u2229 S| = i<\/jats:italic>}, 1 \u2266 i<\/jats:italic> \u2266 k<\/jats:italic>, with s<\/jats:italic>i<\/jats:italic><\/jats:sub> = |S<\/jats:italic>i<\/jats:italic><\/jats:sub>|. Using the concept of insertible vertices<\/jats:italic> and the concept of neighborhood intersections<\/jats:italic>, we prove the following theorem.<\/jats:p>","DOI":"10.1002\/jgt.3190200203","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T16:23:08Z","timestamp":1181233388000},"page":"123-135","source":"Crossref","is-referenced-by-count":5,"title":["Insertible vertices, neighborhood intersections, and hamiltonicity"],"prefix":"10.1002","volume":"20","author":[{"given":"A.","family":"Ainouche","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"I.","family":"Schiermeyer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,6]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(91)90367-B"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190160602"},{"key":"e_1_2_1_4_2","article-title":"A common generalization of Chv\u00e1tal\u2010Erd\u00f6s and Fraisse's sufficient conditions for hamiltonian graphs","author":"Ainouche A.","journal-title":"Discrete Math."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(91)90468-H"},{"key":"e_1_2_1_6_2","unstructured":"J.Bondu Longest paths and cycles in grpahs of high degree. Research Report CORR 80\u201016 Department of Combinatorics and Optimization. University of Waterloo Waterloo Onaario Candaa (1980)."},{"key":"e_1_2_1_7_2","unstructured":"H. J.BroesmaandH. J.Veldman First Twente Workshop on Graphs and Combinatorial Optimization. Private communication (1989)."},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190140414"},{"key":"e_1_2_1_9_2","unstructured":"G.ChenandR. H.Schelp at the Julius Petersen Conference private communication (1990)."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(72)90079-9"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-2.1.69"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(89)90060-9"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(91)90094-I"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190100316"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.2307\/2308928"},{"key":"e_1_2_1_16_2","unstructured":"I.Schiermeyer Long cycles based on degree\u2010sums of independent triples. Proceedings of the First Twente Workshop on Graphs and Combinatorial Optimization University of Twenty The Netherlands (1989)60\u201366."},{"key":"e_1_2_1_17_2","first-page":"49","article-title":"On generalizing a theorem of Fraisse","volume":"29","author":"Schiermeyer I.","year":"1990","journal-title":"Ars Combinato."},{"key":"e_1_2_1_18_2","unstructured":"I.Schiermeyer Neighborhood intersections and Hamiltonicity. Proceedings in Applied Mathematics 54 Graph Theory Combinatorics Algorithms and Applications. Y. Alavi e. a. SIAM (1991)."},{"key":"e_1_2_1_19_2","unstructured":"F.Tian A note on the paper \u201cA new sufficient condition for hamiltonian graph\u201d. Preprint (1989)."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190200203","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190200203","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T21:29:24Z","timestamp":1698355764000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190200203"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,10]]},"references-count":18,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1995,10]]}},"alternative-id":["10.1002\/jgt.3190200203"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190200203","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,10]]}}}