William B. Kinnersley

Extremal Problems for Game Domination Number

In the domination game on a graph

Cops and Robbers is EXPTIME-complete

G

Domination Game: A proof of the

, two players called Dominator and Staller alternately select vertices of

3/5

G

-Conjecture for Graphs with Minimum Degree at Least Two

. Each vertex chosen must strictly increase the number of vertices dominated; the game ends when the chosen set becomes a dominating set of

Lazy Cops and Robbers on Hypercubes

G

The Robber Strikes Back

. Dominator aims to minimize the size of the resulting dominating set, while Staller aims to maximize it. When both players play optimally, the size of the dominating set produced is the game domination number of

The Game Saturation Number of a Graph

G

Bounds on the length of a game of Cops and Robbers

, denoted by

Game brush number

\gamma_g(G)