{"title":"边缘加权图的边缘理想的顺序科恩-麦考莱特性","authors":"Ly Thi Kieu Diem, Nguyên Công Minh, Thanh Vu","doi":"10.1007/s10801-024-01344-9","DOIUrl":null,"url":null,"abstract":"<p>Let <span>\\(I(G,\\textbf{w})\\)</span> be the edge ideal of an edge-weighted graph <span>\\((G,\\textbf{w})\\)</span>. We prove that <span>\\(I(G,\\textbf{w})\\)</span> is sequentially Cohen–Macaulay for all weight functions <span>\\(\\textbf{w}\\)</span> if and only if <i>G</i> is a Woodroofe graph.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The sequentially Cohen–Macaulay property of edge ideals of edge-weighted graphs\",\"authors\":\"Ly Thi Kieu Diem, Nguyên Công Minh, Thanh Vu\",\"doi\":\"10.1007/s10801-024-01344-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <span>\\\\(I(G,\\\\textbf{w})\\\\)</span> be the edge ideal of an edge-weighted graph <span>\\\\((G,\\\\textbf{w})\\\\)</span>. We prove that <span>\\\\(I(G,\\\\textbf{w})\\\\)</span> is sequentially Cohen–Macaulay for all weight functions <span>\\\\(\\\\textbf{w}\\\\)</span> if and only if <i>G</i> is a Woodroofe graph.\\n</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-07-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10801-024-01344-9\",\"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://doi.org/10.1007/s10801-024-01344-9","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
让 \(I(G,\textbf{w})\) 成为边加权图 \((G,\textbf{w})\) 的边理想。我们将证明，当且仅当 G 是一个伍德罗夫图时，\(I(G,\textbf{w})\)对于所有权重函数 \(\textbf{w}\)都是顺序科恩-麦考莱（Cohen-Macaulay）。
The sequentially Cohen–Macaulay property of edge ideals of edge-weighted graphs
Let \(I(G,\textbf{w})\) be the edge ideal of an edge-weighted graph \((G,\textbf{w})\). We prove that \(I(G,\textbf{w})\) is sequentially Cohen–Macaulay for all weight functions \(\textbf{w}\) if and only if G is a Woodroofe graph.
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