N. Smirnov

Deletion and palette size in the domatic number game

Hartnell and Rall recently introduced the domatic number game. Alice and Bob color the vertices of a graph from a palette [\(k\)], and Alice wins if every color class is a dominating set at the end of the game. The largest winning palette size is denoted by \(\mathop{\mathrm{dom}}\nolimits_{g}(G)\) when Alice moves fir...