{"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":"11 6","pages":""},"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}
引用次数: 1
Abstract
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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