{"title":"测试大图中的子图","authors":"N. Alon","doi":"10.1109/SFCS.2001.959918","DOIUrl":null,"url":null,"abstract":"Let H be a fixed graph with h vertices, let G be a graph on n vertices and suppose that at least /spl epsi/n/sup 2/ edges have to be deleted from it to make it H-free. It is known that in this case G contains at least f (/spl epsi/, H)n/sup h/ copies of H. We show that the largest possible function f (/spl epsi/, H) is polynomial in /spl epsi/ if and only if H is bipartite. This implies that there is a one-sided error property tester for checking H-freeness, whose query complexity is polynomial in 1//spl epsi/, if and only if H is bipartite.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"6 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"184","resultStr":"{\"title\":\"Testing subgraphs in large graphs\",\"authors\":\"N. Alon\",\"doi\":\"10.1109/SFCS.2001.959918\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let H be a fixed graph with h vertices, let G be a graph on n vertices and suppose that at least /spl epsi/n/sup 2/ edges have to be deleted from it to make it H-free. It is known that in this case G contains at least f (/spl epsi/, H)n/sup h/ copies of H. We show that the largest possible function f (/spl epsi/, H) is polynomial in /spl epsi/ if and only if H is bipartite. This implies that there is a one-sided error property tester for checking H-freeness, whose query complexity is polynomial in 1//spl epsi/, if and only if H is bipartite.\",\"PeriodicalId\":378126,\"journal\":{\"name\":\"Proceedings 2001 IEEE International Conference on Cluster Computing\",\"volume\":\"6 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-10-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"184\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings 2001 IEEE International Conference on Cluster Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.2001.959918\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings 2001 IEEE International Conference on Cluster Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.2001.959918","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let H be a fixed graph with h vertices, let G be a graph on n vertices and suppose that at least /spl epsi/n/sup 2/ edges have to be deleted from it to make it H-free. It is known that in this case G contains at least f (/spl epsi/, H)n/sup h/ copies of H. We show that the largest possible function f (/spl epsi/, H) is polynomial in /spl epsi/ if and only if H is bipartite. This implies that there is a one-sided error property tester for checking H-freeness, whose query complexity is polynomial in 1//spl epsi/, if and only if H is bipartite.
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