  For an edge-colored graph $G$, the minimum color degree of $G$ means the
minimum number of colors on edges which are adjacent to each vertex of $G$. We
prove that if $G$ is an edge-colored graph with minimum color degree at least
$5$ then $V(G)$ can be partitioned into two parts such that each part induces a
subgraph with minimum color degree at least $2$. We show this theorem by
proving a much stronger form. Moreover, we point out an important relationship
between our theorem and Bermond-Thomassen's conjecture in digraphs.
