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.
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Gendron, B., Hertz, A. and St-Louis, P. (2008) On a Generalization of the Gallai-Roy-Vitaver Theorem to the Bandwidth Coloring Problem. Operations Research Letters, 36, 345-350.
