Open-problem statements, with their sources attached.

WOWII Conjecture 61

For a simple connected graph $G$, the size $f(G)$ of a largest induced forest satisfies $f(G) \ge \mathrm{residue}(G) + \lceil \mathrm{diam}(G) / 3 \rceil$, where $\mathrm{residue}(G)$ is the Havel-Hakimi residue and $\mathrm{diam}(G)$ is the diameter of $G$.

See: Favaron, Mahéo, Saclé (1991) for the residue; DeLaVina's Graffiti.pc for the conjecture.

WOWII Conjecture 65:

For a simple connected graph $G$, the size $f(G)$ of a largest induced forest satisfies $f(G) \ge \operatorname{dist\_min}(A) + \lceil \operatorname{dist\_min}(M) / 3 \rceil$, where $A$ is the set of minimum-degree vertices, $M$ is the set of maximum-degree vertices, and $\operatorname{dist\_min}(S) = \min_{v \notin S} \operatorname{dist}(v, S)$ (see distMin).