{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T06:40:50Z","timestamp":1698043250751},"reference-count":7,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":6517,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1988,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For integers <jats:italic>p<\/jats:italic> and <jats:italic>s<\/jats:italic> satisfying 2 \u2a7d <jats:italic>s<\/jats:italic> \u2a7d p \u2212 1, let <jats:italic>m<\/jats:italic>(<jats:italic>p,s<\/jats:italic>) denote the maximum number of edges in a graph <jats:italic>G<\/jats:italic> of order <jats:italic>p<\/jats:italic> such that the minimum degree in the hamiltonian path graph of <jats:italic>G<\/jats:italic> equals <jats:italic>s<\/jats:italic>. The values of <jats:italic>m<\/jats:italic>(<jats:italic>p, s<\/jats:italic>) are determined for 2 \u2a7d s \u2a7d p\/2 and for (2<jats:italic>p<\/jats:italic> \u2212 2)\/3 \u2a7d <jats:italic>s<\/jats:italic> \u2a7d <jats:italic>p<\/jats:italic> \u2212 1, and upper and lower bounds on <jats:italic>m<\/jats:italic>(<jats:italic>p, s<\/jats:italic>) are obtained for <jats:italic>p<\/jats:italic>\/2 &lt; <jats:italic>s<\/jats:italic> &lt; (2<jats:italic>p<\/jats:italic> \u2212 2)\/3.<\/jats:p>","DOI":"10.1002\/jgt.3190120404","type":"journal-article","created":{"date-parts":[[2007,6,9]],"date-time":"2007-06-09T00:48:10Z","timestamp":1181350090000},"page":"491-497","source":"Crossref","is-referenced-by-count":0,"title":["On minimum degree in Hamiltonian path graphs"],"prefix":"10.1002","volume":"12","author":[{"given":"George R. T.","family":"Hendry","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190070406"},{"key":"e_1_2_1_3_2","volume-title":"Graphs and Digraphs","author":"Chartrand G.","year":"1986"},{"key":"e_1_2_1_4_2","first-page":"189","volume-title":"The Theory and Applications of Graphs","author":"Chartrand G.","year":"1981"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190110312"},{"key":"e_1_2_1_6_2","unstructured":"G. R. T.Hendry On an analogue of Tur\u00e1n's theorem for hamiltonian path graphs submitted."},{"key":"e_1_2_1_7_2","first-page":"21","article-title":"Hamiltonian connected graphs","volume":"42","author":"Ore O.","year":"1963","journal-title":"J. Math. Pure Appl."},{"key":"e_1_2_1_8_2","first-page":"1051","article-title":"Homogeneously traceable and hamiltonian connected graphs","volume":"17","author":"Skupie\u0144 Z.","year":"1984","journal-title":"Demonstratio Math."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190120404","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190120404","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T03:45:29Z","timestamp":1697946329000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190120404"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1988,12]]},"references-count":7,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1988,12]]}},"alternative-id":["10.1002\/jgt.3190120404"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190120404","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1988,12]]}}}