LINEAR SPHERICITY TESTING OF 3-CONNECTED SINGLE SOURCE DIGRAPHS

It has been proved that sphericity testing for digraphs is an NP-complete problem. Here, we investigate sphericity of 3- connected single source digraphs. We provide a new combinatorial characterization of sphericity and give a linear time algorithm for sphericity testing. Our algorithm tests whether a 3-connected single source digraph with n vertices is spherical in O(n) time.