Characterization for Series-Parallel Channel Graphs

A graph G is called an s-stage graph if the set of vertices can be partitioned into s disjoint subsets Vh · · · , Vs, and the set of edges partitioned into s -- 1 disjoint subsets E, · · ·, Es-i, such that edges in Ei connect vertices in V, to vertices in Vt+i. G is called an s-stage channel graph if each of V and Vs contain a single vertex, called the source and the sink, respectively, and if each vertex in V,, 1