The Edge Ideals of Complete Multipartite Hypergraphs

Abstract

We classify all complete uniform multipartite hypergraphs with respect to some algebraic properties, such as being (almost) complete intersection, Gorenstein, level, l-Cohen-Macaulay, l-Buchsbaum, unmixed, and satisfying Serre's condition S r , via some combinatorial terms. Also, we prove that for a complete s-uniform t-partite hypergraph ℋ, vertex decomposability, shellability, sequentially S r , and sequentially Cohen–Macaulay properties coincide with the condition that ℋ has t − 1 sides consisting of a single vertex. Moreover, we show that the latter condition occurs if and only if it is a chordal hypergraph.