  A graph $G$ is called interval colorable if it has a proper edge coloring
with colors $1,2,3,\dots$ such that the colors of the edges incident to every
vertex of $G$ form an interval of integers. Not all graphs are interval
colorable; in fact, quite few families have been proved to admit interval
colorings. In this paper we introduce and investigate a new notion, the
interval coloring thickness of a graph $G$, denoted
${\theta_{\mathrm{int}}}(G)$, which is the minimum number of interval colorable
edge-disjoint subgraphs of $G$ whose union is $G$.
  Our investigation is motivated by scheduling problems with compactness
requirements, in particular, problems whose solution may consist of several
schedules, but where each schedule must not contain any waiting periods or idle
times for all involved parties. We first prove that every connected properly
$3$-edge colorable graph with maximum degree $3$ is interval colorable, and
using this result, we deduce an upper bound on ${\theta_{\mathrm{int}}}(G)$ for
general graphs $G$. We demonstrate that this upper bound can be improved in the
case when $G$ is bipartite, planar or complete multipartite and consider some
applications in timetabling.
