An algorithm for finding all the k-components of a digraph

Abstract

A k-component of a digraph is a maximal subgraph in which k disjoint paths exist between every ordered pair of vertices. A digraph may have many k-components, namely 1-components, 2-components,..., and so on. This paper presents an algorithm to find all the possible k-components of a digraph with n vertices and e edges within 0(n ^∗ max (n+ e,T)time for every k, where T denotes the time bound to find a minimum vertex separator of the digraph. This result is also available for a graph.

Keywords:

• Graph
• digraph
• connectivity
• k-component
• vertex separator
• network flow
• algorithm
• time complexity

C.R. Categories:

• F.2.2
• G.2.2