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.

Lin, C. (2007) Simple Proofs of Results on Paths Representing All Colors in Proper Vertex-Colorings. Graphs and Combinatorics, 23, 201-203. https://doi.org/10.1007/s00373-007-0694-3

Vitaver, L.M. (1962) Determination of Minimal Coloring of Vertices of a Graph by Means of Boolean Powers of the Incidence Matrix (Russian). Doklady Akademii Nauk SSSR, 147, 758-759.

Figueiredo, R.M.V., Barbosa, V.C., Maculan, N. and De Souza, C.C. (2008) A Cyclic Orientations with Path Constraints. RAIRO—Operations Research, 42, 455-467.

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.