Normality of subrings generated by square free monomials (Q1815304)

Let \(\{x_1, \dots, x_n\}\) be the vertex set of a graph \(G\); the ideal \(I(G)\) generated by all the monomials \(x_ix_j\), where \(\{x_i, x_j\}\) is an edge in \(G\), is called the edge ideal of \(G\); \(I(G)\) is a square-free homogeneous ideal, generated in degree 2 and \(G\) is normal if the Rees algebra of \(I(G)\) is normal. The author proves here some results on ideals generated by square free monomials which, in the previous setting, imply that when a graph \(G\) is normal, then also the cone over \(G\) and the suspension of \(G\) are normal. Applications and extensions in the case \(G\) = complete graph are considered.