Intervals of integers modulo n

Question

Do the following related concepts appear anywhere in literature?

1. Denoting an "interval" in the integers modulo $n$ by $[i,j] = \{i, i+1, \dotsc, j\}$. For example, in modulo 6, $[5,3] = \{5,0,1,2,3\}$.
2. Given a collection of intervals $\mathcal{I}$ (e.g. of the above type, or of real numbers), is there a name for the property that for every pair of intersecting intervals $I$ and $J$ in $\mathcal{I}$, either $I \subseteq J$ or $J \subseteq I$?

Answer 1

For 2, if the collection is finite, then you can consider its interval graph, which is a graph representation of the intersections among the intervals in the collection. Now I quote Wikipedia:

The interval graphs that have an interval representation in which every two intervals are either disjoint or nested are the trivially perfect graphs.