Luke Martin, Thomas McKenzie, Shannon Overbay, Lin Ai Tan
{"title":"克莱因书嵌件","authors":"Luke Martin, Thomas McKenzie, Shannon Overbay, Lin Ai Tan","doi":"10.1007/s13370-025-01323-8","DOIUrl":null,"url":null,"abstract":"<div><p>Book embeddings of graphs have been the subject of extensive study. The definitions of such embeddings have been generalized by allowing pages to be cylinders, tori, and Möbius bands rather than half-planes. In this paper, we consider book pages as Klein bottles. We give an application of these Klein books and edge bounds for graphs embeddable in the books. We conclude with optimal Klein book embeddings of some families of graphs.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 2","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Klein book embeddings\",\"authors\":\"Luke Martin, Thomas McKenzie, Shannon Overbay, Lin Ai Tan\",\"doi\":\"10.1007/s13370-025-01323-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Book embeddings of graphs have been the subject of extensive study. The definitions of such embeddings have been generalized by allowing pages to be cylinders, tori, and Möbius bands rather than half-planes. In this paper, we consider book pages as Klein bottles. We give an application of these Klein books and edge bounds for graphs embeddable in the books. We conclude with optimal Klein book embeddings of some families of graphs.</p></div>\",\"PeriodicalId\":46107,\"journal\":{\"name\":\"Afrika Matematika\",\"volume\":\"36 2\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2025-05-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Afrika Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13370-025-01323-8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afrika Matematika","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s13370-025-01323-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Book embeddings of graphs have been the subject of extensive study. The definitions of such embeddings have been generalized by allowing pages to be cylinders, tori, and Möbius bands rather than half-planes. In this paper, we consider book pages as Klein bottles. We give an application of these Klein books and edge bounds for graphs embeddable in the books. We conclude with optimal Klein book embeddings of some families of graphs.