A treatise on pansophy
Is Version Of
In 2017, Boats and Kikas introduced a new parameter, the pansophy of a graph, which is the expected value of the number of disjointly-routable paths in a graph given a random distribution of ordered starting and stopping points. We present an introduction to the topic and prove several results related to pansophy, including formulas and bounds for the pansophies of different graphs
and graph families, the effect of various graph operations, and some density results. We also discuss the computational aspect of computing the pansophy of a graph.