6 problems

Let $G$ be a graph on $n$ vertices with minimum degree at least $2$. The game domination number $\gamma_g(G)$ is the number of moves in the domination game when Dominator starts an…

Let $G$ be a graph on $n$ vertices. A Hamiltonian path is a path containing every vertex of $G$ exactly once. The game domination number $\gamma_g(G)$ is the number of moves in the…

Let $G$ be a graph with $n$ vertices and minimum degree at least $2$. The game domination number $\gamma_g(G)$ is the number of moves in the domination game when Dominator starts a…

Let $G$ be a graph on $n \geq 6$ vertices, with minimum degree at least $2$. The game domination number $\gamma_g(G)$ is the number of moves in the domination game when Dominator s…

Let $G$ be an isolate-free graph of order $n$, and let $\gamma_g(G)$ denote the game domination number, the number of vertices selected when Dominator starts and both players play…

Rall's 1/2-conjecture. If $G$ is traceable, then