New bounds on the number of Edges of the maximal Permutation Graphs

Abstract

In this paper, we bound the number of edges of a maximal permutation graph with n vertices. We propose a new method to compute the lower bound by splitting the set of labellings of the edges into six parts, considering one separate problem for each part, explicitly determining the cardinality of four parts and summing up the corresponding values. We finish with an upper bound of the number of edges of a maximal permutation graph.