A linear-time algorithm to find independent spanning trees in maximal planar graphs

Abstract

Given a graph G, a designated vertex r and a natural number k, we wish to _nd k “independent" spanning trees of G rooted at r, that is, k spanning trees such that, for any vertex v, the k paths connecting r and v in the k trees are internally disjoint in G. In this paper we give a linear-time algorithm to _nd k independent spanning trees in a k-connected maximal planar graph rooted at any designated vertex.