Bujtás–Iršič–Klavžar's strict 3/5 improvement conjecture for the domination game

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 starts and both players play optimally. Bujtás–Iršič–Klavžar's conjecture. There exists a constant $c < 3/5$ such that

$$\gamma_g(G) \leq cn.$$

This conjecture seeks a uniform improvement over the general $3n/5$ upper bound for graphs without isolated vertices, specifically for graphs without leaves. The paper's main theorem gives the bound $10n/17+1/17$, but does not establish the existence of a constant below $3/5$.