{"title":"无限图中的流动","authors":"Jon Folkman, D.R. Fulkerson","doi":"10.1016/S0021-9800(70)80006-0","DOIUrl":null,"url":null,"abstract":"<div><p>A theorem is established that provides necessary and sufficient conditions in order that a locally finite bipartite graph have a subgraph whose valences lie in prescribed intervals. This theorem is applied to the study of flows in locally finite directed graphs. In particular, generalizations of the max-flow min-cut theorem and of the circulation theorem are obtained.</p><p>The axiom of choice is assumed throughout.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"8 1","pages":"Pages 30-44"},"PeriodicalIF":0.0000,"publicationDate":"1970-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80006-0","citationCount":"27","resultStr":"{\"title\":\"Flows in infinite graphs\",\"authors\":\"Jon Folkman, D.R. Fulkerson\",\"doi\":\"10.1016/S0021-9800(70)80006-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A theorem is established that provides necessary and sufficient conditions in order that a locally finite bipartite graph have a subgraph whose valences lie in prescribed intervals. This theorem is applied to the study of flows in locally finite directed graphs. In particular, generalizations of the max-flow min-cut theorem and of the circulation theorem are obtained.</p><p>The axiom of choice is assumed throughout.</p></div>\",\"PeriodicalId\":100765,\"journal\":{\"name\":\"Journal of Combinatorial Theory\",\"volume\":\"8 1\",\"pages\":\"Pages 30-44\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1970-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80006-0\",\"citationCount\":\"27\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021980070800060\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021980070800060","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A theorem is established that provides necessary and sufficient conditions in order that a locally finite bipartite graph have a subgraph whose valences lie in prescribed intervals. This theorem is applied to the study of flows in locally finite directed graphs. In particular, generalizations of the max-flow min-cut theorem and of the circulation theorem are obtained.
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