5 problems

Andrews et al.'s conjecture. If $G$ is a connected graph of order at least $3$ that is not a $5$-cycle, then

Group twin chromatic index conjecture. We conjecture that

Araújo–Cohen–Giroire–Havet conjecture. There is no critical graph with average degree less than $3$, with the exception of $C_3$ and $K_{2,3}$.

Modified Araújo–Cohen–Giroire–Havet conjecture. There is no critical graph with average degree less than $3$, with the exception of $C_3$, $K_{2,3}$, and $H$.

Modified Araújo–Cohen–Giroire–Havet conjecture. For every $c<4$, the number of pairwise non-isomorphic critical graphs with girth at least five and average degree at most $c$ is fi…