The theta-pyramid-prism-turtle minimal separator conjecture

A graph is a finite undirected graph, and a minimal separator is a vertex set that minimally separates some pair of vertices. Theta-pyramid-prism-turtle conjecture. There is a polynomial $P$ such that every graph $G$ that contains no theta, pyramid, prism, or turtle has at most $P(|V(G)|)$ minimal separators. This conjecture asks whether forbidding these four graph configurations guarantees polynomially many minimal separators; the paper presents it as a conjecture from the cited work, and its status is not resolved here.