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Optimizing weakly triangulated graphs

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Abstract

A graph is weakly triangulated if neither the graph nor its complement contains a chordless cycle with five or more vertices as an induced subgraph. We use a new characterization of weakly triangulated graphs to solve certain optimization problems for these graphs. Specifically, an algorithm which runs inO((n + e)n 3) time is presented which solves the maximum clique and minimum colouring problems for weakly triangulated graphs; performing the algorithm on the complement gives a solution to the maximum stable set and minimum clique covering problems. Also, anO((n + e)n 4) time algorithm is presented which solves the weighted versions of these problems.

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References

  1. Berge, C.: Färbung von Graphen deren sämtliche bzw. ungerade Kreise starr sind (Zusammenfassung). Wiss. Z. Martin-Luther-Univ. Halle-Winterberg, Math.-Natur. Reihe, 114 (1961)

  2. Berge, C. Chvátal, V.:Topics on perfect graphs, Ann. Discrete Math.21, (1984)

  3. Cook, S.A.: The complexity of theorem-proving procedure. In: Proceedings of the Third Annual ACM Symposium on Theory of Computing, Assoc. Comp. Mach., New York, 151–158 (1971)

  4. Grötschel, M., Lovász, L. Schrijver, A.: Polynomial algorithms for perfect graphs. In: [2, pp. 325–356]

  5. Hayward, R.: Weakly triangulated graphs. J. Comb. Theory (B)39, 200–208 (1985)

    Google Scholar 

  6. Hayward, R.: Two classes of perfect graphs. Doctoral thesis, School of Computer Science, McGill University (1987)

  7. Karp, R.: Reducibility among combinatorial problems. In: Complexity of Computer Computations (by R. Miller and J. Thatcher) pp. 85–103 New York: Plenum Press (1972)

    Google Scholar 

  8. Meyniel, H.: A new property of critical imperfect graphs and some consequences. Europ. J. Comb.8, 313–316 (1987)

    Google Scholar 

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Authors and Affiliations

  1. Computer Science Department, Rutgers University, 08903, New Brunswick, NJ, USA

    Ryan Hayward & Chính Hoàng

  2. Rutgers Center for Operations Research, Rutgers University, 08903, New Brunswick, NJ, USA

    Frédéric Maffray

Authors
  1. Ryan Hayward
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  2. Chính Hoàng
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  3. Frédéric Maffray
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Additional information

The author acknowledges the support of an N.S.E.R.C. Canada postgraduate scholarship.

The author acknowledges the support of the U.S. Air Force Office of Scientific Research under grant number AFOSR 0271 to Rutgers University.

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Hayward, R., Hoàng, C. & Maffray, F. Optimizing weakly triangulated graphs. Graphs and Combinatorics 5, 339–349 (1989). https://doi.org/10.1007/BF01788689

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  • DOI: https://doi.org/10.1007/BF01788689

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