{"title":"Forced Edges and Graph Structure.","authors":"Brian Cloteaux","doi":"10.6028/jres.124.022","DOIUrl":null,"url":null,"abstract":"<p><p>For a degree sequence, we define the set of edges that appear in every labeled realization of that sequence as forced, while the edges that appear in none are define as forbidden. We examine the structure of graphs in which the degree sequences contain either forced or forbidden edges. The results include the determination of the structure of the forced or forbidden edge sets, the relationship between the sizes of forced and forbidden sets for a sequence, and the structural consequences to their realizations. This includes showing that the diameter of every realization of a degree sequence containing forced or forbidden edges is no greater than 3, and that these graphs are maximally edge-connected.</p>","PeriodicalId":54766,"journal":{"name":"Journal of Research of the National Institute of Standards and Technology","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2019-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.6028/jres.124.022","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Research of the National Institute of Standards and Technology","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.6028/jres.124.022","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2019/1/1 0:00:00","PubModel":"eCollection","JCR":"Q3","JCRName":"INSTRUMENTS & INSTRUMENTATION","Score":null,"Total":0}
引用次数: 2
Abstract
For a degree sequence, we define the set of edges that appear in every labeled realization of that sequence as forced, while the edges that appear in none are define as forbidden. We examine the structure of graphs in which the degree sequences contain either forced or forbidden edges. The results include the determination of the structure of the forced or forbidden edge sets, the relationship between the sizes of forced and forbidden sets for a sequence, and the structural consequences to their realizations. This includes showing that the diameter of every realization of a degree sequence containing forced or forbidden edges is no greater than 3, and that these graphs are maximally edge-connected.
期刊介绍：
The Journal of Research of the National Institute of Standards and Technology is the flagship publication of the National Institute of Standards and Technology. It has been published under various titles and forms since 1904, with its roots as Scientific Papers issued as the Bulletin of the Bureau of Standards.
In 1928, the Scientific Papers were combined with Technologic Papers, which reported results of investigations of material and methods of testing. This new publication was titled the Bureau of Standards Journal of Research.
The Journal of Research of NIST reports NIST research and development in metrology and related fields of physical science, engineering, applied mathematics, statistics, biotechnology, information technology.
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