{"title":"The maximum size of a nonhamiltonian-connected graph with given order and minimum degree","authors":"Leilei Zhang","doi":"arxiv-2409.10255","DOIUrl":null,"url":null,"abstract":"In this paper, we determine the maximum size of a nonhamiltonian-connected\ngraph with prescribed order and minimum degree. We also characterize the\nextremal graphs that attain this maximum size. This work generalizes a previous\nresult obtained by Ore [ J. Math. Pures Appl. 42 (1963) 21-27] and further\nextends a theorem proved by Ho, Lin, Tan, Hsu, and Hsu [Appl. Math. Lett. 23\n(2010) 26-29]. As a corollary of our main result, we determine the maximum size\nof a $k$-connected nonhamiltonian-connected graph with a given order.","PeriodicalId":501407,"journal":{"name":"arXiv - MATH - Combinatorics","volume":"7 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10255","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we determine the maximum size of a nonhamiltonian-connected
graph with prescribed order and minimum degree. We also characterize the
extremal graphs that attain this maximum size. This work generalizes a previous
result obtained by Ore [ J. Math. Pures Appl. 42 (1963) 21-27] and further
extends a theorem proved by Ho, Lin, Tan, Hsu, and Hsu [Appl. Math. Lett. 23
(2010) 26-29]. As a corollary of our main result, we determine the maximum size
of a $k$-connected nonhamiltonian-connected graph with a given order.
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