Complete Multipartite Graphs are Pansophical

Abstract

Given a graph $G$, we are interested in finding disjoint paths for a given set of distinct pairs of vertices. In 2017, we formally defined a new parameter, the pansophy of $G$, in the context of the disjoint path problem.

In this paper, we construct a method to determine the pansophy of any complete bipartite graph, and then generalize the method to compute the pansophy of any complete multipartite graph. We close with future research directions.