6 problems

Bounded nonrepetitive connection conjecture. There exists a constant $t$ such that every $2$-connected graph $G$ satisfies

Let $G$ be a graph of maximum degree $\Delta$. The Thue chromatic index conjecture. There is a constant $C$ such that … Here, $\pi'(G)$ is the minimum number of colors in a nonrepe…

Facial Thue choice number conjecture. There exists a constant $C$ such that

Grytczuk's conjecture. There is a constant $c$ such that

A graph has page number $k$ if its vertices can be arranged on a spine and its edges partitioned into $k$ pages, with no two edges on the same page crossing in the spine order. A v…

Let $G$ be a plane graph, meaning a graph together with a fixed embedding in the plane. A facial path is a sequence of consecutive vertices on the boundary of a face, and a vertex…