{"title":"关于中间层定理的一本书的证明","authors":"Torsten Mütze","doi":"10.1007/s00493-023-00070-3","DOIUrl":null,"url":null,"abstract":"<p>We give a short constructive proof for the existence of a Hamilton cycle in the subgraph of the <span>\\((2n+1)\\)</span>-dimensional hypercube induced by all vertices with exactly <i>n</i> or <span>\\(n+1\\)</span> many 1s.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A Book Proof of the Middle Levels Theorem\",\"authors\":\"Torsten Mütze\",\"doi\":\"10.1007/s00493-023-00070-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We give a short constructive proof for the existence of a Hamilton cycle in the subgraph of the <span>\\\\((2n+1)\\\\)</span>-dimensional hypercube induced by all vertices with exactly <i>n</i> or <span>\\\\(n+1\\\\)</span> many 1s.</p>\",\"PeriodicalId\":50666,\"journal\":{\"name\":\"Combinatorica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-11-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Combinatorica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00493-023-00070-3\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Combinatorica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00493-023-00070-3","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We give a short constructive proof for the existence of a Hamilton cycle in the subgraph of the \((2n+1)\)-dimensional hypercube induced by all vertices with exactly n or \(n+1\) many 1s.
期刊介绍：
COMBINATORICA publishes research papers in English in a variety of areas of combinatorics and the theory of computing, with particular emphasis on general techniques and unifying principles. Typical but not exclusive topics covered by COMBINATORICA are
- Combinatorial structures (graphs, hypergraphs, matroids, designs, permutation groups).
- Combinatorial optimization.
- Combinatorial aspects of geometry and number theory.
- Algorithms in combinatorics and related fields.
- Computational complexity theory.
- Randomization and explicit construction in combinatorics and algorithms.
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