{"title":"On Arc Reversal in Digraphs With a Restricted Number of Cycles","authors":"Z. R. Bogdanowicz","doi":"10.47443/cm.2022.014","DOIUrl":null,"url":null,"abstract":"Let C G be a longest cycle in the directed graph G = ( V, A ) . Let q be the total number of cycles in G . It is proved that if 1 ≤ q ≤ | V ( C G ) | then there exists an arc a ∈ A ( G ) whose reversal decreases the total number of cycles in G .","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.47443/cm.2022.014","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Let C G be a longest cycle in the directed graph G = ( V, A ) . Let q be the total number of cycles in G . It is proved that if 1 ≤ q ≤ | V ( C G ) | then there exists an arc a ∈ A ( G ) whose reversal decreases the total number of cycles in G .
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