REGULARITY AND GROBNER BASES OF THE REES ALGEBRA OF EDGE IDEALS OF BIPARTITE GRAPHS

Let G be a bipartite graph and I = I(G) be its edge ideal. The aim of this note is to investigate different aspects of the Rees algebra R(I) of I. We compute its regularity and the universal Grobner basis of its defining equations; interestingly, both of them are described in terms of the combinatorics of G. We apply these ideas to study the regularity of the powers of I. For any s >= match(G) + vertical bar E (G)vertical bar + 1 we prove that reg(Is+1) = reg(I-s) + 2.