4 problems

Nevries–Rosenke's conjecture. The leaf powers are exactly the strongly chordal graphs that contain none of $H_1,\ldots,H_7$ as an induced subgraph.

Finite-obstruction conjecture for fixed $k$. For fixed $k$, the class $\mathcal{L}(k)$ may be characterized by a finite set of obstructions.

Let $G=(V,E)$ be a strongly chordal graph, and let ${{\cal A}}(G)=({{\cal X}},{{\cal E}})$ be its clique arrangement. A bad $2$-cycle is a bad cycle of length $2$ in this clique ar…

Let $G_7$ be the strongly chordal graph described in the paper that is not a leaf power, and let a forbidden induced subgraph of leaf powers mean a graph that is not a leaf power b…