3 problems

Equitable-factorization characterization conjecture. If $G$ is a $k$-tree-connected graph, then $G$ admits a $k$-equitable factorization if and only if, for every…

Almost equitable factorization conjecture. The graph $G$ can be edge-decomposed into factors $G_1,\ldots,G_k$ such that, for every $v\in V(G)$,

Odd-degree planar edge-partition conjecture. The edges of $G$ can be partitioned into $\tfrac{\Delta-1}{2}$ linear forests and one matching.