# Substitution decomposition on chordal graphs and applications

Conference paper

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## Abstract

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^{2}) to O(n+m). We also devise a simple linear time algorithm for interval graph recognition where no complicated data structure is involved.

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© Springer-Verlag Berlin Heidelberg 1991