Output-polynomial enumeration for incomparability graphs of $S_t$-free posets

Let $t$ be a positive integer. A poset is $S_t$-free if it contains no suborder isomorphic to the poset $S_t$, and let $\textsc{Dom-Enum}$ denote the problem of enumerating all minimal dominating sets of a graph.

The $S_t$-free incomparability conjecture. For every $t$, there is an output-polynomial time algorithm for $\textsc{Dom-Enum}$ in incomparability graphs of $S_t$-free posets.

The result would extend the paper's bounded-dimension algorithm to a broader class of posets. The proposed extension is not covered by the current proof, which relies crucially on a bounded-dimension representation; the conjecture remains open.