Fast and Simple Algorithms for Recognizing Chordal Comparability Graphs and Interval Graphs

In this paper, we present a linear-time algorithm for substitution decomposition on chordal graphs. Based on this result, we develop a linear-time algorithm for transitive orientation on chordal comparability graphs, which reduces the complexity of chordal comparability recognition from O(n) to O(n+m). We also devise a simple linear-time algorithm for interval graph recognition where no complicated data structure is involved.