{"title":"n-Hamiltonian graphs","authors":"Gary Chartrand , S.F. Kapoor, Don R. Lick","doi":"10.1016/S0021-9800(70)80069-2","DOIUrl":null,"url":null,"abstract":"<div><p>A graph <em>G</em> with <em>p</em>≥3 points, 0≤<em>n</em>≤<em>p</em>−3, is called <em>n</em>-Hamiltonian if the removal of any <em>k</em> points from <em>G</em>, 0≤<em>k≤n</em>, results in a Hamiltonian graph. This generalizes the concept of Hamiltonian graphs in as much as the 0-Hamiltonian graphs are precisely the Hamiltonian graphs. Sufficient conditions for a graph to be <em>n</em>-Hamiltonian are presented, including generalizations of results on Hamiltonian graphs due to Dirac, Ore, and Pósa.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"9 3","pages":"Pages 308-312"},"PeriodicalIF":0.0000,"publicationDate":"1970-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80069-2","citationCount":"29","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021980070800692","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 29
Abstract
A graph G with p≥3 points, 0≤n≤p−3, is called n-Hamiltonian if the removal of any k points from G, 0≤k≤n, results in a Hamiltonian graph. This generalizes the concept of Hamiltonian graphs in as much as the 0-Hamiltonian graphs are precisely the Hamiltonian graphs. Sufficient conditions for a graph to be n-Hamiltonian are presented, including generalizations of results on Hamiltonian graphs due to Dirac, Ore, and Pósa.
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