In this paper, we show that every $(3k-3)$-edge-connected graph $G$, under a certain condition on whose degrees, can be edge-decomposed into $k$ factors $G_1,\ldots, G_k$ such that for each vertex $v\in V(G_i)$, $|d_{G_i}(v)-d_G(v)/k|< 1$, where $1\le i\le k$. As application, we deduce that every $6$-edge-connected graph $G$ can be edge-decomposed into three factors $G_1$, $G_2$, and $G_3$ such that for each vertex $v\in V(G_i)$, $|d_{G_i}(v)-d_{G}(v)/3|< 1$, unless $G$ has exactly one vertex… Expand