On Nordhaus-Gaddum type inequalities for the game chromatic and game coloring numbers

A seminal result by Nordhaus and Gaddum states that 2 root n <= chi(G) + chi((G) over bar) <= n + 1 for every graph G of order n, where (G) over bar is the complement of G and chi is the chromatic number. We study similar inequalities for chi(g)(G) and col(g)(G), which denote, respectively, the game chromatic number and the game coloring number of G. Those graph invariants give the score for, respectively, the coloring and marking games on G when both players use their best strategies. (C) 2019 Elsevier B.V. All rights reserved.