King and Pelsmajer's bounded-exception domination conjecture for plane triangulations

Let $G$ be an $n$-vertex plane triangulation, and let $t$ be a fixed nonnegative integer. A vertex has degree other than $6$ when its degree in $G$ is not equal to $6$. A dominating set is a set of vertices such that every vertex is either in the set or adjacent to a vertex in the set.

King and Pelsmajer's conjecture. For any constant $t$, there exists $n_t$ such that every $n$-vertex plane triangulation with $n>n_t$ and at most $t$ vertices of degree other than $6$ has a dominating set of size at most $n/4$.

This extends the previously studied maximum-degree-at-most-$6$ case to triangulations with only a bounded number of exceptional-degree vertices. The paper states this as a conjecture and subsequently proves a stronger bound under the same bounded-exception hypothesis.