  A proper edge-coloring of a graph is an interval coloring if the labels on
the edges incident to any vertex form an interval of consecutive integers.
Interval thickness s(G) of a graph G is the smallest number of interval
colorable graphs edge-decomposing G. We prove that s(G)=o(n) for any graph G on
n vertices. This improves the previously known bound of 2n/5 by Asratian,
Casselgren, and Petrosyan. While we do not have a single example of a graph
with interval thickness strictly greater than 2, we construct bipartite graphs
whose interval spectrum has arbitrarily many arbitrarily large gaps. Here, an
interval 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.
