Spanning subgraphs of k-connected digraphs

https://doi.org/10.1016/0095-8956(81)90087-3Get rights and content
Under an Elsevier user license
open archive

Abstract

It is shown that every k-edge-connected digraph with m edges and n vertices contains a spanning connected subgraph having at most 2m + 6(k −1)(n − 1))(5k − 3) edges. When k = 2 the bound is improved to (3m + 8(n − 1))10, which implies that a 2-edge-connected digraph is connected by less than 70% of its edges. Examples are given which require almost two-thirds of the edges to connect all vertices.

Cited by (0)

This research was supported by National Science Foundation Grant MPS 75-08325.