关于超图的簇覆盖的一些结果和问题

Pub Date : 2024-06-11 DOI:10.1002/jgt.23111

Vojtech Rödl, Marcelo Sales

{"title":"关于超图的簇覆盖的一些结果和问题","authors":"Vojtech Rödl, Marcelo Sales","doi":"10.1002/jgt.23111","DOIUrl":null,"url":null,"abstract":"For a <math>\n <semantics>\n <mrow>\n <mi>k</mi>\n </mrow>\n <annotation> $k$</annotation>\n </semantics></math>-uniform hypergraph <math>\n <semantics>\n <mrow>\n <mi>F</mi>\n </mrow>\n <annotation> $F$</annotation>\n </semantics></math> we consider the parameter <math>\n <semantics>\n <mrow>\n <mi>Θ</mi>\n <mrow>\n <mo>(</mo>\n \n <mi>F</mi>\n \n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation> ${\\rm{\\Theta }}(F)$</annotation>\n </semantics></math>, the minimum size of a clique cover of the edge set of <math>\n <semantics>\n <mrow>\n <mi>F</mi>\n </mrow>\n <annotation> $F$</annotation>\n </semantics></math>. We derive bounds on <math>\n <semantics>\n <mrow>\n <mi>Θ</mi>\n <mrow>\n <mo>(</mo>\n \n <mi>F</mi>\n \n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation> ${\\rm{\\Theta }}(F)$</annotation>\n </semantics></math> for <math>\n <semantics>\n <mrow>\n <mi>F</mi>\n </mrow>\n <annotation> $F$</annotation>\n </semantics></math> belonging to various classes of hypergraphs.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23111","citationCount":"0","resultStr":"{\"title\":\"Some results and problems on clique coverings of hypergraphs\",\"authors\":\"Vojtech Rödl, Marcelo Sales\",\"doi\":\"10.1002/jgt.23111\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For a <math>\\n <semantics>\\n <mrow>\\n <mi>k</mi>\\n </mrow>\\n <annotation> $k$</annotation>\\n </semantics></math>-uniform hypergraph <math>\\n <semantics>\\n <mrow>\\n <mi>F</mi>\\n </mrow>\\n <annotation> $F$</annotation>\\n </semantics></math> we consider the parameter <math>\\n <semantics>\\n <mrow>\\n <mi>Θ</mi>\\n <mrow>\\n <mo>(</mo>\\n \\n <mi>F</mi>\\n \\n <mo>)</mo>\\n </mrow>\\n </mrow>\\n <annotation> ${\\\\rm{\\\\Theta }}(F)$</annotation>\\n </semantics></math>, the minimum size of a clique cover of the edge set of <math>\\n <semantics>\\n <mrow>\\n <mi>F</mi>\\n </mrow>\\n <annotation> $F$</annotation>\\n </semantics></math>. We derive bounds on <math>\\n <semantics>\\n <mrow>\\n <mi>Θ</mi>\\n <mrow>\\n <mo>(</mo>\\n \\n <mi>F</mi>\\n \\n <mo>)</mo>\\n </mrow>\\n </mrow>\\n <annotation> ${\\\\rm{\\\\Theta }}(F)$</annotation>\\n </semantics></math> for <math>\\n <semantics>\\n <mrow>\\n <mi>F</mi>\\n </mrow>\\n <annotation> $F$</annotation>\\n </semantics></math> belonging to various classes of hypergraphs.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-06-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23111\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/jgt.23111\",\"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.23111","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

对于一个 k $k$ 的均匀超图 F $F$ ，我们考虑参数 Θ ( F ) ${rm{\Theta }}(F)$ ，即 F $F$ 边集的簇覆盖的最小大小。我们推导出属于各种超图类别的 F $F$ 的 Θ ( F ) ${\rm{\Theta }}(F)$ 的边界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

Some results and problems on clique coverings of hypergraphs

For a $k$ -uniform hypergraph $F$ we consider the parameter $Θ (F)$ , the minimum size of a clique cover of the edge set of $F$ . We derive bounds on $Θ (F)$ for $F$ belonging to various classes of hypergraphs.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助