{"title":"超图二次着色的改进界和算法","authors":"J. Radhakrishnan, A. Srinivasan","doi":"10.1109/SFCS.1998.743519","DOIUrl":null,"url":null,"abstract":"We show that for all large n, every n-uniform hypergraph with at most 0.7/spl radic/(n/lnn)/spl times/2/sup n/ edges can be two-colored. We, in fact, present fast algorithms that output a proper two-coloring with high probability for such hypergraphs. We also derandomize and parallelize these algorithms, to derive NC/sup 1/ versions of these results. This makes progress on a problem of Erdos (1963), improving the previous-best bound of n/sup 1/3-0(1)//spl times/2/sup n/ due to Beck (1978). We further generalize this to a \"local\" version, improving on one of the first applications of the Lovasz Local Lemma.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1998-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"14","resultStr":"{\"title\":\"Improved bounds and algorithms for hypergraph two-coloring\",\"authors\":\"J. Radhakrishnan, A. Srinivasan\",\"doi\":\"10.1109/SFCS.1998.743519\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that for all large n, every n-uniform hypergraph with at most 0.7/spl radic/(n/lnn)/spl times/2/sup n/ edges can be two-colored. We, in fact, present fast algorithms that output a proper two-coloring with high probability for such hypergraphs. We also derandomize and parallelize these algorithms, to derive NC/sup 1/ versions of these results. This makes progress on a problem of Erdos (1963), improving the previous-best bound of n/sup 1/3-0(1)//spl times/2/sup n/ due to Beck (1978). We further generalize this to a \\\"local\\\" version, improving on one of the first applications of the Lovasz Local Lemma.\",\"PeriodicalId\":228145,\"journal\":{\"name\":\"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)\",\"volume\":\"17 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1998-11-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"14\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.1998.743519\",\"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 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1998.743519","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Improved bounds and algorithms for hypergraph two-coloring
We show that for all large n, every n-uniform hypergraph with at most 0.7/spl radic/(n/lnn)/spl times/2/sup n/ edges can be two-colored. We, in fact, present fast algorithms that output a proper two-coloring with high probability for such hypergraphs. We also derandomize and parallelize these algorithms, to derive NC/sup 1/ versions of these results. This makes progress on a problem of Erdos (1963), improving the previous-best bound of n/sup 1/3-0(1)//spl times/2/sup n/ due to Beck (1978). We further generalize this to a "local" version, improving on one of the first applications of the Lovasz Local Lemma.
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