Interval graphs also play an important role in temporal reasoning.

From this construction one can verify a common property held by all interval graphs.

Threshold graphs are also a special case of interval graphs.

The connected triangle-free interval graphs are exactly the caterpillar trees.

Interval graphs are used to represent resource allocation problems in operations research and scheduling theory.

The complement of any interval graph is a comparability graph.

Every claw-free graph is not necessarily a proper interval graph.

Cohen applied interval graphs to mathematical models of population biology, specifically food webs.

For interval graphs this bound is tight.

Interval graphs are integral to some algorithms used in compilers, specifically data flow analyses.

The intersection graph of a set of intervals on a line is called the interval graph.

Circular-arc graphs are a natural generalization of interval graphs.

In that context, he also posed the specific case of intersecting intervals on a line, namely the now classical family of interval graphs.

Interval graphs are chordal graphs and hence perfect graphs.

For example, when assigning aircraft to flights, the resulting conflict graph is an interval graph, so the coloring problem can be solved efficiently.

A graph constructed from a multigraph by replacing each edge by a fuzzy linear interval graph.

Another parameter, the graph bandwidth, has an analogous definition from proper interval graphs, and is at least as large as the pathwidth.

The intersection number of an interval graph is always equal to its number of maximal cliques, which may be computed in polynomial time.

Interval graphs are exactly the graphs that are chordal and that have comparability graph complements.

Interval graphs are the intersection graphs of subtrees of path graphs, a special case of trees.

They are a class of co-comparability graphs that contain interval graphs and permutation graphs as subclasses.

Finding a set of intervals that represent an interval graph can also be used as a way of assembling contiguous subsequences in DNA mapping.

A tighter bound is possible for interval graphs, and more generally chordal graphs: in these graphs there can be at most n maximal cliques.

An interval graph is defined as the intersection graph of intervals on the real line, or of connected subgraphs of a path graph.

Alternatively, the pathwidth may be defined from interval graphs analogously to the definition of treewidth from chordal graphs.