The edge ideals of complete multipartite hypergraphs [article]

Dariush Kiani, Sara Saeedi Madani
2014 arXiv   pre-print
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
more » ... of a single vertex. Moreover, we show that the latter condition occurs if and only if it is a chordal hypergraph.
arXiv:1402.2469v1 fatcat:syt3aeujvfdfdhs4cye7nwgweq