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…

Let $G$ be a bipartite graph, let $k\ge 3$ and $m$ be positive integers, and let $f:V(G)\rightarrow Z_k$ be a compatible mapping. The bipartite tree-connected factor conjecture. If…

Let $G$ be a graph with $|V(G)|\ge 2$, let $z_0\in V(G)$, and let $k$ be a positive integer. Let $p:V(G)\rightarrow Z_k$ satisfy … For each vertex $v$, choose an integer…