Length of the Longest Path and Diameter in Orientations of Graphs

Abstract

We say that a parameter p of directed graphs has the interval property if for every graph G and orientations of G, p can take every value between its minimum and maximum values. Let λ be the length of the longest directed path. A question asked by C. Lin in [1] is equivalent to the question of whether λ has the interval property. In this note, we answer this question in the affirmative. We also show that the diameter of directed graphs does not have the interval property.