The Pansophy of Semi Directed Graphs

Given an ordered list of randomly-selected pairs of vertices in a graph, how many of these pairs can be connected with disjoint paths? The pansophy of a graph G is the expected number of possible disjoint paths—this has been calculated and studied for many classes of undirected graphs. In this chapter we study the pansophy of various graphs where an edge or a select collection of edges have been directed. By doing this, how is the pansophy of G affected? Do specific selections of edges affect pansophy differently from other selections? These and other questions are addressed in this chapter.