4 problems

Eventual equality conjecture. For each $n \in \mathbb{N}$, there is an $N \in \mathbb{N}$ such that

Let a gucycle be a cyclic ordering whose windows represent each isomorphism class of graphs on $n$ vertices exactly once. Corrected gucycle conjecture. For each $n\geq 4$, there ex…

Let a gucycle be a cyclic ordering whose windows represent each isomorphism class of graphs on $n$ vertices exactly once. Brockman–Kay–Snively's conjecture. For each $n\neq 2$, the…

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 gra…