| Vertex Decomposable Property of Graphs Whose Complements Are $r$-Partite |
| Received:January 09, 2020 Revised:September 06, 2020 |
| Key Words:
vertex decomposable graph Cohen-Macaulay graph complement $r$-partite
|
| Fund Project:Supported by the Natural Science Foundation of Shanghai (Grant No.19ZR1424100) and the National Natural Science Foundation of China (Grant No.11971338). |
|
| Hits: 708 |
| Download times: 585 |
| Abstract: |
| 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 $r\ge 4$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2021.01.003 |
| View Full Text View/Add Comment |
