On Dyadic Fractional Packings of $T$-Joins

Abstract

Let G = (V,E) be a graph, and T ⊆ V a nonempty subset of even cardinality. The famous theorem of Edmonds and Johnson on the T -join polyhedron implies that the minimum cardinality of a T -cut is equal to the maximum value of a fractional packing of T -joins. In this paper, we prove that the fractions assigned may be picked as dyadic rationals, i.e. of the form a 2k for some integers a, k ≥ 0.