The LBFS Structure and Recognition of Interval Graphs

A graph is an interval graph if it is the intersection graph of intervals on a line. Interval graphs are known to be the intersection of chordal graphs and asteroidal triple-free graphs, two families where the well-known Lexicographic Breadth First Search (LBFS) plays an important algorithmic and structural role. In this paper we show that interval graphs have a very rich LBFS structure and that, by exploiting this structure, one can design a linear time, easily implementable, interval graph recognition algorithm.