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An Introduction to Chordal Graphs and Clique Trees

  • Conference paper
Graph Theory and Sparse Matrix Computation

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 56))

Abstract

Clique trees and chordal graphs have carved out a niche for themselves in recent work on sparse matrix algorithms, due primarily to research questions associated with advanced computer architectures. This paper is a unified and elementary introduction to the standard characterizations of chordal graphs and clique trees. The pace is leisurely, as detailed proofs of all results are included. We also briefly discuss applications of chordal graphs and clique trees in sparse matrix computations.

Work was supported in part by the Applied Mathematical Sciences Research Program, Office of Energy Research, U.S. Department of Energy under contract DE-ACO5-840R21400 with Martin Marietta Energy Systems, Incorporated, and in part by the Institute for Mathematics and Its Applications with funds provided by the National Science Foundation.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Tennessee, Knoxville, TN, 37996-1301, USA

    Jean R. S. Blair

  2. Mathematical Sciences Section, Oak Ridge National Laboratory, P.O. Box 2008, Bldg. 6012, Oak Ridge, TN, 37831-6367, USA

    Barry Peyton

Authors
  1. Jean R. S. Blair
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  2. Barry Peyton
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Editor information

Editors and Affiliations

  1. University of Waterloo, Needles Hall, Waterloo, Ontario, N2L 3G1, Canada

    Alan George

  2. Xerox Palo Alto Research Center, 3333 Coyote Hill Road, Palo Alto, CA, 94304-1314, USA

    John R. Gilbert

  3. Department of Computer Science, York University, North York, Ontario, M3J 1P3, Canada

    Joseph W. H. Liu

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© 1993 Springer-Verlag New York, Inc.

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Blair, J.R.S., Peyton, B. (1993). An Introduction to Chordal Graphs and Clique Trees. In: George, A., Gilbert, J.R., Liu, J.W.H. (eds) Graph Theory and Sparse Matrix Computation. The IMA Volumes in Mathematics and its Applications, vol 56. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8369-7_1

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  • DOI: https://doi.org/10.1007/978-1-4613-8369-7_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8371-0

  • Online ISBN: 978-1-4613-8369-7

  • eBook Packages: Springer Book Archive

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