On integer multiflows and metric packings in matroids

Abstract

Seymour [10] has characterized graphs and more generally matroids in which the simplest possible necessary condition, the “cut condition”, is also sufficient for multiflow feasibility. In this work we exhibit the next level of necessary conditions, three conditions which correspond in a well-defined way to minimally non-ideal binary clutters. We characterize the subclass of matroids where the presented conditions are also sufficient for multiflow feasibility, and prove the existence of integer multiflows for Eulerian weights. The theorem we prove uses results from Seymour[10] and generalizes those results and those in Schwärzler, Sebő