A proper edge‐coloring of a graph is an interval coloring if the labels on the edges incident to any vertex form an interval, that is, form a set of consecutive integers. The interval coloring thickness θ(G) of a graph G is the smallest number of interval colorable graphs edge‐decomposing G . We prove that θ(G)=o(n) for any graph G on n vertices. This improves the previously known bound of 2[n/5], see Asratian, Casselgren, and Petrosyan. While we do not have a single example of a graph with an interval coloring thickness strictly greater than 2, we construct bipartite graphs whose interval coloring spectrum has arbitrarily many arbitrarily large gaps. Here, an interval coloring spectrum of a graph is the set of all integers t such that the graph has an interval coloring using t colors. Interval colorings of bipartite graphs naturally correspond to no‐wait schedules, say for parent–teacher conferences, where a conversation between any teacher and any parent lasts the same amount of time. Our results imply that any such conference with n participants can be coordinated in o(n) no‐wait periods. In addition, we show that for any integers t and T,t<T , there is a set of pairs of parents and teachers wanting to talk to each other, such that any no‐wait schedules are unstable—they could last t hours and could last T hours, but there is no possible no‐wait schedule lasting x hours if t<x<T