On Nordhaus–Gaddum type inequalities for the game chromatic and game coloring numbers - Archive ouverte HAL
Article Dans Une Revue Discrete Mathematics Année : 2019

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

Résumé

A seminal result by Nordhaus and Gaddum states that 2n≤χ(G)+χ(G¯)≤n+1 for every graph G of order n, where G¯ is the complement of G and χ is the chromatic number. We study similar inequalities for χg(G) and colg(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.

Dates et versions

hal-02320062 , version 1 (18-10-2019)

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Citer

Clément Charpentier, Simone Dantas, Celina M.H. de Figueiredo, Ana Furtado, Sylvain Gravier. On Nordhaus–Gaddum type inequalities for the game chromatic and game coloring numbers. Discrete Mathematics, 2019, 342 (5), pp.1318-1324. ⟨10.1016/j.disc.2019.01.012⟩. ⟨hal-02320062⟩
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