List coloring and diagonal coloring for plane graphs of diameter two.

Let G be a maximal plane graph of diameter at most two. Let χ l (G) and χ d (G) denote the list chromatic number and the diagonal chromatic number of G , respectively. In this paper, we study the structure of G and show the following results: (1) χ l (G) ≤ 4; and (2) χ d (G) ≤ 9, and χ d (G) = 9 if and only if G is a specific graph on nine vertices. [ABSTRACT FROM AUTHOR]