SEQUENTIALLY COHEN-MACAULAY GRAPHS OF FORM θN1 ,...,NK
Fatemeh Mohammadi, Dariush Kiani · 2011
Abstract. Let k be an integer greater than 2 and n1,..., nk be a sequence of positive integers with at most one of them being equal to 1. Let θn1,...,nk be a graph consisting of k paths, having only their endpoints in common. We characterize all sequentially Cohen-Macaulay graphs of this type. We also show for these types of graphs the notions of vertex decomposable, shellable and sequen-tially Cohen-Macaulay are equivalent. 1.