4 problems

Let $\mathcal{F}$ be a finite set of graphs, and let an $\mathcal{F}$-free graph be a graph with no induced subgraph isomorphic to a member of $\mathcal{F}$. Let $\mathcal{S}$ be t…

Independent-planar-minor MIS conjecture. For every planar $H$ and every $k$, MIS is polynomial-time solvable on the class of $kH$-free graphs.

Gartland's conjecture. For every planar graph $H$, MIS admits a polynomial-time algorithm on $H$-induced-minor-free graphs.

Polynomial-time MWIS conjecture. The problem \textsc{MWIS}\ is solvable in polynomial time on $H$-free graphs.