A Construction of Sequentially Cohen-Macaulay Graphs  

作　　者：Aming Liu Tongsuo Wu 

机构地区：[1]School of Science,Hainan University,Haikou 570228,China [2]School of Mathematical Sciences,Shanghai Jiao Tong University Shanghai 200240,China

出　　处：《Algebra Colloquium》2021年第3期399-414,共16页代数集刊（英文版）

基　　金：Supported by the Natural Science Foundation of Shanghai(No.19ZR1424100);the National Natural Science Foundation of China(No.11271250,11971338).

摘　　要：For every simple graph G,a class of multiple clique cluster-whiskered graphs G^(eπm)is introduced,and it is shown that all such graphs are vertex decomposable;thus,the independence simplicial complex Ind G^(eπm)is sequentially Cohen-Macaulay.The properties of the graphs G^(eπm)and G^(π)constructed by Cook and Nagel are studied,including the enumeration of facets of the complex Ind G^(π)and the calculation of Betti numbers of the cover ideal Ic(G^(eπm).We also prove that the complex△=IndH is strongly shellable and pure for either a Boolean graph H=Bn or the full clique-whiskered graph H=G^(W)of C,which is obtained by adding a whisker to each vertex of G.This implies that both the facet ideal I(△)and the cover ideal Ic(H)have linear quotients.

关 键 词：multiple clique cluster-whiskered graph vertex decomposable strongly shell-able Boolean graph facet ideal 

分 类 号：O15[理学—数学]