ON SMALL CUTS SEPARATING AN ABELIAN CAYLEY GRAPH INTO 2 EQUAL PARTS

Let Gamma be a connected directed Cayley graph with outdegree r. We sh ow that there is a cutset of size < (4n ln(n/2))/D whose deletion crea tes a sink B and a source (B) over bar such that \B\ = (B) over bar. I n particular Gamma can be separated into two equal parts by deleting l ess than (8e/r)n(?(l-1/r)) ln(n/2) vertices. Our results improve a rec ent one proved by Annexstein and Baumslag [1]. As a main tool, we use inequalities from additive number theory.