An Algorithm for Packing Connectors

Given an undirected graph G = (V; E) and a partition fS; Tg of V , an S{T connector is a set of edges F E such that every component of the subgraph (V; F) intersects both S and T. If either S or T is a singleton, then an S{T connector is a spanning tree of G. On the other hand, if G is bipartite with colour classes S and T, then an S{T connector is an edge cover of G (a set of edges covering all vertices). An S{T connector is a common spanning set of two graphic ma-troids on E. We prove a theorem on packing common spanning sets of certain matroids, generalizing a result of Davies and McDiarmid on strongly base orderable matroids. As a corollary, we obtain an O((n; m) + nm) time algorithm for nding a maximum number of S{T connectors, where (n; m) denotes the complexity of nding a maximum number of edge disjoint spanning trees in a graph on n vertices and m edges. Since the best known bound for (n; m) is O(nm log(m=n)), this bound for packing S{T connectors is as good as the current bound for packing spanning trees.