{"title":"图的完全强迫数","authors":"Xin He, Heping Zhang","doi":"10.26493/1855-3974.2706.3c8","DOIUrl":null,"url":null,"abstract":"The complete forcing number of a graph G with a perfect matching is the minimum cardinality of an edge set of G on which the restriction of each perfect matching M is a forcing set of M . This concept can be view as a strengthening of the concept of global forcing number of G . Do ˇ sli ´ c (2007) obtained that the global forcing number of a connected graph is at most its cyclomatic number. Motivated from this result, we obtain that the complete forcing number of a graph is no more than 2 times its cyclomatic number and characterize the matching covered graphs whose complete forcing numbers attain this upper bound and minus one, respectively. Besides, we present a method of constructing a complete forcing set of a graph. By using such method, we give closed formulas for the complete forcing numbers of wheels and cylinders.","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Complete forcing numbers of graphs\",\"authors\":\"Xin He, Heping Zhang\",\"doi\":\"10.26493/1855-3974.2706.3c8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The complete forcing number of a graph G with a perfect matching is the minimum cardinality of an edge set of G on which the restriction of each perfect matching M is a forcing set of M . This concept can be view as a strengthening of the concept of global forcing number of G . Do ˇ sli ´ c (2007) obtained that the global forcing number of a connected graph is at most its cyclomatic number. Motivated from this result, we obtain that the complete forcing number of a graph is no more than 2 times its cyclomatic number and characterize the matching covered graphs whose complete forcing numbers attain this upper bound and minus one, respectively. Besides, we present a method of constructing a complete forcing set of a graph. By using such method, we give closed formulas for the complete forcing numbers of wheels and cylinders.\",\"PeriodicalId\":8402,\"journal\":{\"name\":\"Ars Math. Contemp.\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-07-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ars Math. Contemp.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26493/1855-3974.2706.3c8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ars Math. Contemp.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26493/1855-3974.2706.3c8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The complete forcing number of a graph G with a perfect matching is the minimum cardinality of an edge set of G on which the restriction of each perfect matching M is a forcing set of M . This concept can be view as a strengthening of the concept of global forcing number of G . Do ˇ sli ´ c (2007) obtained that the global forcing number of a connected graph is at most its cyclomatic number. Motivated from this result, we obtain that the complete forcing number of a graph is no more than 2 times its cyclomatic number and characterize the matching covered graphs whose complete forcing numbers attain this upper bound and minus one, respectively. Besides, we present a method of constructing a complete forcing set of a graph. By using such method, we give closed formulas for the complete forcing numbers of wheels and cylinders.
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