文摘
Let G be a finite simple graph. We give a lower bound for the Castelnuovo–Mumford regularity of the toric ideal IGIG associated to G in terms of the sizes and number of induced complete bipartite graphs in G. When G is a chordal bipartite graph, we find an upper bound for the regularity of IGIG in terms of the size of the bipartition of G . We also give a new proof for the graded Betti numbers of the toric ideal associated to the complete bipartite graph K2,nK2,n.