{"title":"克莱因瓶 II 不包括未成年人。级联","authors":"Bojan Mohar , Petr Škoda","doi":"10.1016/j.jctb.2023.12.006","DOIUrl":null,"url":null,"abstract":"<div><p>Graphs that are critical (minimal excluded minors) for embeddability in surfaces are studied. In Part I, it was shown that graphs that are critical for embeddings into surfaces of Euler genus <em>k</em><span> or for embeddings into nonorientable surface of genus </span><em>k</em><span><span> are built from 3-connected components, called hoppers and cascades. In Part II, all cascades for Euler genus 2 are classified. As a consequence, the complete list of obstructions of connectivity 2 for embedding graphs into the </span>Klein bottle is obtained.</span></p></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Excluded minors for the Klein bottle II. Cascades\",\"authors\":\"Bojan Mohar , Petr Škoda\",\"doi\":\"10.1016/j.jctb.2023.12.006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Graphs that are critical (minimal excluded minors) for embeddability in surfaces are studied. In Part I, it was shown that graphs that are critical for embeddings into surfaces of Euler genus <em>k</em><span> or for embeddings into nonorientable surface of genus </span><em>k</em><span><span> are built from 3-connected components, called hoppers and cascades. In Part II, all cascades for Euler genus 2 are classified. As a consequence, the complete list of obstructions of connectivity 2 for embedding graphs into the </span>Klein bottle is obtained.</span></p></div>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-01-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0095895624000017\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0095895624000017","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
研究了对嵌入曲面至关重要的图形（最小排除最小）。在第一部分中，研究表明对于嵌入欧拉属 k 的曲面或嵌入属 k 的不可定向曲面至关重要的图形是由 3 个相连的分量构建而成的，这些分量被称为跳板和级联。在第二部分中，将对欧拉属 2 的所有级联进行分类。因此，可以得到将图形嵌入克莱因瓶的连通性 2 的完整障碍列表。
Graphs that are critical (minimal excluded minors) for embeddability in surfaces are studied. In Part I, it was shown that graphs that are critical for embeddings into surfaces of Euler genus k or for embeddings into nonorientable surface of genus k are built from 3-connected components, called hoppers and cascades. In Part II, all cascades for Euler genus 2 are classified. As a consequence, the complete list of obstructions of connectivity 2 for embedding graphs into the Klein bottle is obtained.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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