{"title":"西摩 6 流定理的另一个证明","authors":"Matt DeVos, Jessica McDonald, Kathryn Nurse","doi":"10.1002/jgt.23091","DOIUrl":null,"url":null,"abstract":"<p>In 1981 Seymour proved his famous 6-flow theorem asserting that every 2-edge-connected graph has a nowhere-zero flow in the group <span></span><math>\n \n <mrow>\n <msub>\n <mi>Z</mi>\n \n <mn>2</mn>\n </msub>\n \n <mo>×</mo>\n \n <msub>\n <mi>Z</mi>\n \n <mn>3</mn>\n </msub>\n </mrow></math> (in fact, he offers two proofs of this result). In this note, we give a new short proof of a generalization of this theorem where <span></span><math>\n \n <mrow>\n <msub>\n <mi>Z</mi>\n \n <mn>2</mn>\n </msub>\n \n <mo>×</mo>\n \n <msub>\n <mi>Z</mi>\n \n <mn>3</mn>\n </msub>\n </mrow></math>-valued functions are found subject to certain boundary constraints.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23091","citationCount":"0","resultStr":"{\"title\":\"Another proof of Seymour's 6-flow theorem\",\"authors\":\"Matt DeVos, Jessica McDonald, Kathryn Nurse\",\"doi\":\"10.1002/jgt.23091\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In 1981 Seymour proved his famous 6-flow theorem asserting that every 2-edge-connected graph has a nowhere-zero flow in the group <span></span><math>\\n \\n <mrow>\\n <msub>\\n <mi>Z</mi>\\n \\n <mn>2</mn>\\n </msub>\\n \\n <mo>×</mo>\\n \\n <msub>\\n <mi>Z</mi>\\n \\n <mn>3</mn>\\n </msub>\\n </mrow></math> (in fact, he offers two proofs of this result). In this note, we give a new short proof of a generalization of this theorem where <span></span><math>\\n \\n <mrow>\\n <msub>\\n <mi>Z</mi>\\n \\n <mn>2</mn>\\n </msub>\\n \\n <mo>×</mo>\\n \\n <msub>\\n <mi>Z</mi>\\n \\n <mn>3</mn>\\n </msub>\\n </mrow></math>-valued functions are found subject to certain boundary constraints.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-04-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23091\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/jgt.23091\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/jgt.23091","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In 1981 Seymour proved his famous 6-flow theorem asserting that every 2-edge-connected graph has a nowhere-zero flow in the group (in fact, he offers two proofs of this result). In this note, we give a new short proof of a generalization of this theorem where -valued functions are found subject to certain boundary constraints.
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