{"title":"具有任意周长的非哈密顿3{正则图","authors":"M. Haythorpe","doi":"10.13189/UJAM.2014.020111","DOIUrl":null,"url":null,"abstract":"It is well known that 3-regular graphs with arbitrarily large girth exist. Three constructions are given that use the former to produce non-Hamiltonian 3-regular graphs without reducing the girth, thereby proving that such graphs with arbitrarily large girth also exist. The resulting graphs can be 1-, 2- or 3-edge-connected de- pending on the construction chosen. From the constructions arise (naive) upper bounds on the size of the smallest non-Hamiltonian 3-regular graphs with particular girth. Several examples are given of the smallest such graphs for various choices of girth and connectedness.","PeriodicalId":372283,"journal":{"name":"Universal Journal of Applied Mathematics","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Non-Hamiltonian 3{Regular Graphs with Arbitrary Girth\",\"authors\":\"M. Haythorpe\",\"doi\":\"10.13189/UJAM.2014.020111\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is well known that 3-regular graphs with arbitrarily large girth exist. Three constructions are given that use the former to produce non-Hamiltonian 3-regular graphs without reducing the girth, thereby proving that such graphs with arbitrarily large girth also exist. The resulting graphs can be 1-, 2- or 3-edge-connected de- pending on the construction chosen. From the constructions arise (naive) upper bounds on the size of the smallest non-Hamiltonian 3-regular graphs with particular girth. Several examples are given of the smallest such graphs for various choices of girth and connectedness.\",\"PeriodicalId\":372283,\"journal\":{\"name\":\"Universal Journal of Applied Mathematics\",\"volume\":\"8 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-02-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Universal Journal of Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.13189/UJAM.2014.020111\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Universal Journal of Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.13189/UJAM.2014.020111","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Non-Hamiltonian 3{Regular Graphs with Arbitrary Girth
It is well known that 3-regular graphs with arbitrarily large girth exist. Three constructions are given that use the former to produce non-Hamiltonian 3-regular graphs without reducing the girth, thereby proving that such graphs with arbitrarily large girth also exist. The resulting graphs can be 1-, 2- or 3-edge-connected de- pending on the construction chosen. From the constructions arise (naive) upper bounds on the size of the smallest non-Hamiltonian 3-regular graphs with particular girth. Several examples are given of the smallest such graphs for various choices of girth and connectedness.
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