On small cuts separating an abelian Cayley graph into two equal parts

Abstract

Let Γ be a connected directed Cayley graph with outdegreer. We show that there is a cutset of size ≤ (4n In(n/2))/D whose deletion creates a sinkB and a sourceB such that ¦B¦ = ¦B¦. In particular Γ can be separated into two equal parts by deleting less than (8e/r)n ^(1-1/r) In(n/2) vertices. Our results improve a recent one proved by Annexstein and Baumslag [1]. As a main tool, we use inequalities from additive number theory.