{"title":"无立方顶点的多面体是棱-汉密尔顿多面体","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":"{\"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}","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}
Polyhedra without cubic vertices are prism-hamiltonian
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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