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A Fully Dynamic Graph Algorithm for Recognizing Interval Graphs

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Abstract

We present the first dynamic graph algorithm for recognizing interval graphs. The algorithm runs in O(nlog n) worst-case time per edge deletion or edge insertion, where n is the number of vertices in the graph. The algorithm uses a new representation of interval graphs called the train tree, which is based on the clique-separator graph representation of chordal graphs. The train tree has a number of useful properties and it can be constructed from the clique-separator graph in O(n) time.

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Authors and Affiliations

  1. College of Computing and Digital Media, DePaul University, 243 S. Wabash Ave., Chicago, IL, 60604, USA

    Louis Ibarra

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  1. Louis Ibarra
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Correspondence to Louis Ibarra.

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Most of the results in this paper were part of the author’s Ph.D. Thesis at the University of Victoria.

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Ibarra, L. A Fully Dynamic Graph Algorithm for Recognizing Interval Graphs. Algorithmica 58, 637–678 (2010). https://doi.org/10.1007/s00453-009-9291-6

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  • DOI: https://doi.org/10.1007/s00453-009-9291-6

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