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
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Fund Project:Supported by the Natural Science Foundation of Shanghai (Grant No.19ZR1424100) and the National Natural Science Foundation of China (Grant No.11971338). |
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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 |
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