15 problems

Let $G$ be a random graph, and let $\gamma_{MB}(G,b)$ and $s_{MB}(G,b)$ denote the two Maker–Breaker domination game parameters. For a Binomial random graph $G_{n,p}$ with constant…

Tree three-sevenths conjecture. If $T$ is a tree of order $n\geq 3$, then

Minimum-degree three-sevenths conjecture. If $\delta(G)\geq 2$, then

Three-sevenths upper-bound conjecture. For any graph $G$ with no $K_2$-components,

Consider a simple undirected graph $G$ with vertex set $V(G)$ and order $n=|V(G)|$. The game domination number $\gamma_g(G)$ is the value of the domination game on $G$ when Dominat…

Let $G$ be a graph. It is minimally $\gamma_g$-imperfect if $G$ is not $\gamma_g$-perfect, while every proper induced subgraph of $G$ is $\gamma_g$-perfect. The anti-holes…

Let $G$ be a graph without isolated vertices, and let $n(G)$ denote its order. The L-domination game number of $G$ is denoted by $\gamma_{Lg}(G)$. The 6/7-conjecture. … This is an…

Let $G$ be a graph, and let ${\gamma_{g}^{t}}(G)$ denote the number of vertices chosen when Dominator starts the game total domination game on $G$. Three-fourths conjecture. For ev…

Upper-bound conjecture. The correct upper bound for $gamma_{{\rm tg}}(G)$ is $3n/4$.

The $3/5$-Game Domination Conjecture.

The $3/4$-Game Total Domination Conjecture.

3/5-conjecture.

Generalized Kinnersley–West–Zamani 3/5-conjecture. For every isolate-free graph $G$ of order $n$,

Kinnersley–West–Zamani 3/5-conjecture.

Tree domination-game pair conjecture. No pair of the form $(k,k-1)$ can be realized by a tree.