{"title":"Polyhedra without cubic vertices are prism-hamiltonian","authors":"Simon Špacapan","doi":"10.1002/jgt.23078","DOIUrl":null,"url":null,"abstract":"<p>The prism over a graph <span></span><math>\n <semantics>\n <mrow>\n <mi>G</mi>\n </mrow>\n <annotation> $G$</annotation>\n </semantics></math> is the Cartesian product of <span></span><math>\n <semantics>\n <mrow>\n <mi>G</mi>\n </mrow>\n <annotation> $G$</annotation>\n </semantics></math> with the complete graph on two vertices. A graph <span></span><math>\n <semantics>\n <mrow>\n <mi>G</mi>\n </mrow>\n <annotation> $G$</annotation>\n </semantics></math> is prism-hamiltonian if the prism over <span></span><math>\n <semantics>\n <mrow>\n <mi>G</mi>\n </mrow>\n <annotation> $G$</annotation>\n </semantics></math> is hamiltonian. We prove that every polyhedral graph (i.e., 3-connected planar graph) of minimum degree at least four is prism-hamiltonian.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23078","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/jgt.23078","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
The prism over a graph is the Cartesian product of with the complete graph on two vertices. A graph is prism-hamiltonian if the prism over is hamiltonian. We prove that every polyhedral graph (i.e., 3-connected planar graph) of minimum degree at least four is prism-hamiltonian.
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