{"title":"(g, f)-因子存在的邻域条件","authors":"Haruhide Matsuda","doi":"10.5036/MJIU.36.1","DOIUrl":null,"url":null,"abstract":"We obtain a sufficient condition for the existence of a (g, f)-factor in terms of vertex-deleted subgraphs. The following theorem is proved: Let G be a graph, k an even integer, g, f: V(G)→\\mathbb{Z} two functions such that g(x)≤f(x) for all x∈V(G), and {u0, u1, …, uk/2} the set of distinct vertices of G such that {u1, u2, …, uk/2}⊆NG(u0). If g(u0)≤k≤f(u0) and G-{ui} has a (g, f)-factor for all i=0, …, k/2, then G has a (g, f)-factor.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"20 1","pages":"1-4"},"PeriodicalIF":0.0000,"publicationDate":"2004-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Neighborhood conditions for the existence of ( g, f )-factors\",\"authors\":\"Haruhide Matsuda\",\"doi\":\"10.5036/MJIU.36.1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We obtain a sufficient condition for the existence of a (g, f)-factor in terms of vertex-deleted subgraphs. The following theorem is proved: Let G be a graph, k an even integer, g, f: V(G)→\\\\mathbb{Z} two functions such that g(x)≤f(x) for all x∈V(G), and {u0, u1, …, uk/2} the set of distinct vertices of G such that {u1, u2, …, uk/2}⊆NG(u0). If g(u0)≤k≤f(u0) and G-{ui} has a (g, f)-factor for all i=0, …, k/2, then G has a (g, f)-factor.\",\"PeriodicalId\":18362,\"journal\":{\"name\":\"Mathematical Journal of Ibaraki University\",\"volume\":\"20 1\",\"pages\":\"1-4\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Journal of Ibaraki University\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5036/MJIU.36.1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Journal of Ibaraki University","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5036/MJIU.36.1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Neighborhood conditions for the existence of ( g, f )-factors
We obtain a sufficient condition for the existence of a (g, f)-factor in terms of vertex-deleted subgraphs. The following theorem is proved: Let G be a graph, k an even integer, g, f: V(G)→\mathbb{Z} two functions such that g(x)≤f(x) for all x∈V(G), and {u0, u1, …, uk/2} the set of distinct vertices of G such that {u1, u2, …, uk/2}⊆NG(u0). If g(u0)≤k≤f(u0) and G-{ui} has a (g, f)-factor for all i=0, …, k/2, then G has a (g, f)-factor.
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