12 problems

Conjecture on diagonal-flip stabilization. The only surfaces $S$ for which

Esperet et al.'s flow reconfiguration conjecture. For each graph $G$ and each positive integer $k$,

Let $G$ be a graph, let $\operatorname{diam}(G)$ denote its inversion diameter, and let $\Delta(G)$ denote its maximum degree. Havet et al.'s inversion diameter conjecture. Every g…

Let $G$ be a graph, and let $\mathcal{F}(G,\mathbb{Z}_2^k)$ denote the reconfiguration graph of nowhere-zero $\mathbb{Z}_2^k$-flows. A nowhere-zero $\mathbb{Z}_2^k$-flow…

Let $G$ be a graph, and let $\mathcal{F}(G,A)$ denote its reconfiguration graph whose vertices are nowhere-zero $A$-flows, with adjacency given by changing flow values only on a cy…

Let $G$ be a graph, and let $\mathcal{F}(G,k)$ denote its reconfiguration graph whose vertices are nowhere-zero $k$-flows, with adjacency given by changing flow values only on a cy…

The non-optimal edge-coloring equivalence conjecture. Any two non-optimal colorings are equivalent.

The $(\Delta(G)+2)$-edge-coloring equivalence conjecture. All $(\Delta(G)+2)$-edge-colorings of a graph $G$ are equivalent.

Vizing's conjecture. Every $k$-edge-coloring of a graph $G$ is equivalent to a $\Delta(G)$-edge-coloring of $G$ if there is any.

Cubic-scale diameter conjecture.

List-recoloring conjecture. If either

Six-color conjecture. $R_6(G)$ has diameter $O(n)$.