{"title":"On even matroids","authors":"W. T. Tutte","doi":"10.6028/JRES.071B.028","DOIUrl":null,"url":null,"abstract":"It is s hown in [1] I that e very graphic matroid is regular ([1], 5.63) and even ([IJ, 9.23). Moreover a regular matroid c an be charac terized as a binary one which has no minor of either of the types called BI and BII. ([11. 7.51). In the prese nt paper we es tablish a converse theore m: any ever: matroid whic h has no minor of Type BI mu st be graphi c. 1. Let Y be an atom of a binary matroid M, and suppose it to have the following properties. (i) Y is brid~e-separable (ii) If 8 is any bridge of Y in M , then M X (B U Y) is graphic. Then M is g raphic.","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1967-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.6028/JRES.071B.028","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 9
Abstract
It is s hown in [1] I that e very graphic matroid is regular ([1], 5.63) and even ([IJ, 9.23). Moreover a regular matroid c an be charac terized as a binary one which has no minor of either of the types called BI and BII. ([11. 7.51). In the prese nt paper we es tablish a converse theore m: any ever: matroid whic h has no minor of Type BI mu st be graphi c. 1. Let Y be an atom of a binary matroid M, and suppose it to have the following properties. (i) Y is brid~e-separable (ii) If 8 is any bridge of Y in M , then M X (B U Y) is graphic. Then M is g raphic.
在[1]1中表明，非常图形化的矩阵是正则的([1]，5.63)和偶的([IJ, 9.23)。此外，正则矩阵c可以被表征为一个二元矩阵，它没有BI和BII这两种类型的子矩阵。([11。7.51)。本文建立了一个逆定理:任何不含BI型的任意矩阵都是图1。设Y是二元矩阵M的一个原子，并假定它具有下列性质。(i) Y是桥~e可分的(ii)如果8是M中Y的任意桥，则M X (B U Y)是图形的。那么M是图形的。
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