On K-partitioning the n-cube

Abstract

Let an edge cut partition the vertex set of the n-cube into k subsets A1,⋯, Ak with ||Ai| - |Aj|| ≤ 1. We consider the problem to determine minimal size of such a cut and present its asymptotic as n, k → ∞ and also as n → ∞ and k is a constant of the form k = 2 a ± 2b with a ≥ b ≥ 0.