12 problems

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…

Let $G$ be a finite graph, let $n(G)$ denote its order, let $\delta(G)$ denote its minimum degree, and let $\gamma_g(G)$ denote its game domination number. Sub-three-fifths conject…

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

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 a finite graph, let $n(G)$ denote its order, let $\delta(G)$ denote its minimum degree, and let $\gamma_g(G)$ denote its game domination number. Additive one-half bound.…

Let $G$ be a finite graph, let $n(G)$ denote its order, let $\delta(G)$ denote its minimum degree, and let $\gamma_g(G)$ denote its game domination number. The one-half conjecture…

3/5-Graph Conjecture. If $G$ is isolate-free, then

Three-legged spider criticality conjecture. The tree $T_{p,q,r}$ is $(2(p+q+r)+1)$-$\gamma_g$-critical.

Let $G$ be an isolate-free graph on $n$ vertices. The D-game domination number $\gamma_g(G)$ is the total number of vertices chosen when Dominator starts and both players play opti…