Vertex Decomposable Property of Graphs Whose Complements Are $r$-Partite
Received:January 09, 2020  Revised:September 06, 2020
Key Word: vertex decomposable graph   Cohen-Macaulay   graph complement   $r$-partite  
Fund ProjectL:Supported by the Natural Science Foundation of Shanghai (Grant No.19ZR1424100) and the National Natural Science Foundation of China (Grant No.11971338).
Author NameAffiliation
Saba YASMEEN School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, P. R. China 
Tongsuo WU School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, P. R. China 
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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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