Universal-cycle conjecture for isomorphism classes of graphs

Let $k$ be a positive integer. A U-cycle of isomorphism classes of graphs on $k$ nodes is a cyclic sequence in which every $k$-window represents a distinct isomorphism class of graphs on $k$ nodes, and every such isomorphism class occurs as a window. Universal-cycle conjecture. For each $k \geq 3$, there exists a U-cycle of isomorphism classes of graphs on $k$ nodes. The conjecture proposes a canonical universal-cycle construction for unlabeled graphs; the paper notes that the cases $k=3$ and $k=4$ are possible, while existence for all $k \geq 3$ remains open.