{"title":"科恩-麦考莱双方形图的◦运算和＊运算","authors":"Yulong Yang, Guangjun Zhu, Yijun Cui, Shiya Duan","doi":"10.21136/cmj.2024.0438-23","DOIUrl":null,"url":null,"abstract":"<p>Let <i>G</i> be a finite simple graph with the vertex set <i>V</i> and let <i>I</i><sub><i>G</i></sub> be its edge ideal in the polynomial ring <span>\\(S=\\mathbb{K}[V]\\)</span>. We compute the depth and the Castelnuovo-Mumford regularity of <i>S</i>/<i>I</i><sub><i>G</i></sub> when <i>G</i> = <i>G</i><sub>1</sub> ◦ <i>G</i><sub>2</sub> or <i>G</i> = <i>G</i><sub>1</sub> * <i>G</i><sub>2</sub> is a graph obtained from Cohen-Macaulay bipartite graphs <i>G</i><sub>1</sub>, <i>G</i><sub>2</sub> by the ◦ operation or * operation, respectively.</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"58 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The ◦ operation and * operation of Cohen-Macaulay bipartite graphs\",\"authors\":\"Yulong Yang, Guangjun Zhu, Yijun Cui, Shiya Duan\",\"doi\":\"10.21136/cmj.2024.0438-23\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <i>G</i> be a finite simple graph with the vertex set <i>V</i> and let <i>I</i><sub><i>G</i></sub> be its edge ideal in the polynomial ring <span>\\\\(S=\\\\mathbb{K}[V]\\\\)</span>. We compute the depth and the Castelnuovo-Mumford regularity of <i>S</i>/<i>I</i><sub><i>G</i></sub> when <i>G</i> = <i>G</i><sub>1</sub> ◦ <i>G</i><sub>2</sub> or <i>G</i> = <i>G</i><sub>1</sub> * <i>G</i><sub>2</sub> is a graph obtained from Cohen-Macaulay bipartite graphs <i>G</i><sub>1</sub>, <i>G</i><sub>2</sub> by the ◦ operation or * operation, respectively.</p>\",\"PeriodicalId\":50596,\"journal\":{\"name\":\"Czechoslovak Mathematical Journal\",\"volume\":\"58 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2024-07-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Czechoslovak Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.21136/cmj.2024.0438-23\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Czechoslovak Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.21136/cmj.2024.0438-23","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
设 G 是顶点集为 V 的有限简单图，设 IG 是它在（S=\mathbb{K}[V]\）多项式环中的边理想。当 G = G1 ◦ G2 或 G = G1 * G2 分别是由科恩-马科莱双向图 G1、G2 通过 ◦ 操作或 * 操作得到的图时，我们计算 S/IG 的深度和卡斯特诺沃-蒙福德正则性。
The ◦ operation and * operation of Cohen-Macaulay bipartite graphs
Let G be a finite simple graph with the vertex set V and let IG be its edge ideal in the polynomial ring \(S=\mathbb{K}[V]\). We compute the depth and the Castelnuovo-Mumford regularity of S/IG when G = G1 ◦ G2 or G = G1 * G2 is a graph obtained from Cohen-Macaulay bipartite graphs G1, G2 by the ◦ operation or * operation, respectively.
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