Let Formula: see text be an integer. The Formula: see text-hued chromatic number Formula: see text of a graph Formula: see text is the minimum Formula: see text such that Formula: see text admits a proper Formula: see text-coloring where each vertex Formula: see text has at least Formula: see text distinct colors in its neighborhood. In this paper, we prove that if Formula: see text is a maximal planar graphs with diameter two, then Formula: see text, Formula: see text, Formula: see text, Formula: see text, and Formula: see text if Formula: see text. These upper bounds are sharp. The result confirms the r-hued coloring conjecture proposed by Song at al. in Discrete Math. 315 (2014) 47-52 for maximal planar graphs with diameter two.
Duan et al. (Fri,) studied this question.