On the dimension of the minimal vertex cover semigroup ring of an unmixed bipartite graph

Abstract

In a paper in 2008, Herzog, Hibi and Ohsugi introduced and studied the semigroup ring associated to the set of minimal vertex covers of an unmixed bipartite graph. In this paper we relate the dimension of this semigroup ring to the rank of the Boolean lattice associated to the graph.

Keywords

• Unmixed graph
• bipartite graph
• vertex cover algebra