  A heterochromatic (or rainbow) graph is an edge-colored graph whose edges
have distinct colors, that is, where each color appears at most once. In this
paper, I propose a $(g,f)$-chromatic graph as an edge-colored graph where each
color $c$ appears at least $g(c)$ times and at most $f(c)$ times. I also
present a necessary and sufficient condition for edge-colored graphs (not
necessary to be proper) to have a $(g,f)$-chromatic spanning tree. Using this
criterion, I show that an edge-colored complete graph $G$ has a spanning tree
with a color probability distribution `similar' to that of $G$. Moreover, I
conjecture that an edge-colored complete graph $G$ of order $2n$ $(n \ge 3)$
can be partitioned into $n$ edge-disjoint spanning trees such that each has a
color probability distribution `similar' to that of $G$.
