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

Vertex Decomposable Property of Graphs Whose Complements Are $r$-Partite

DOI：10.3770/j.issn:2095-2651.2021.01.003

 作者 单位 Saba YASMEEN 上海交通大学数学学院, 上海 200240 武同锁 上海交通大学数学学院, 上海 200240

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.

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 $r\ge 4$.