Saba YASMEEN,武同锁.补图是$r$-部的图的顶点可分解性质[J].数学研究及应用,2021,41(1):14~24 |
补图是$r$-部的图的顶点可分解性质 |
Vertex Decomposable Property of Graphs Whose Complements Are $r$-Partite |
投稿时间:2020-01-09 修订日期:2020-09-06 |
DOI:10.3770/j.issn:2095-2651.2021.01.003 |
中文关键词: 顶点可分解图 Cohen-Macaulay性 图的补 $r$-部图 |
英文关键词:vertex decomposable graph Cohen-Macaulay graph complement $r$-partite |
基金项目:海市自然科学基金(Grant No.19ZR1424100),国家自然科学基金(Grant No.11971338). |
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中文摘要: |
假设$G$是一个非完全的简单图,并假设其补图$\bar{G}$是$r$-部图.本文研究这类图的具有(序列)Cohen-Macaulay性质的子类,特别是在$r=2,3$情形,给出了具有该性质的几种构造;在$r\ge 4$ 情形,给出了一些充分条件. |
英文摘要: |
Let $G$ be a non-complete graph such that its complement $\ol{G}$ is $r$-partite. In this paper, properties of the graph $G$ are studied, including the Cohen-Macaulay property and the sequential Cohen-Macaulay property. For $r=2,3$, some constructions are established for $G$ to be \vd\, and some sufficient conditions are provided for $r\ge 4$. |
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