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Finding and counting given length cycles

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Abstract

We present an assortment of methods for finding and counting simple cycles of a given length in directed and undirected graphs. Most of the bounds obtained depend solely on the number of edges in the graph in question, and not on the number of vertices. The bounds obtained improve upon various previously known results.

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References

  1. N. Alon, R. Yuster, and U. Zwick. Finding and counting given length cycles.Proceedings of the 2nd European Symposium on Algorithms, Utrecht, Lecture Notes in Computer Science, Vol. 855, pages 354–364. Springer-Verlag, 1994.

  2. N. Alon, R. Yuster, and U. Zwick. Color-coding.Journal of the ACM, 42:844–856, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  3. B. Bollobás. On generalized graphs.Acta Mathematica Academiae Scientarium Hungaricae, 16:447–452, 1965.

    Article  MATH  Google Scholar 

  4. B. Bollobás.Extremal Graph Theory. Academic Press, New York, 1978.

    MATH  Google Scholar 

  5. J. A. Bondy and M. Simonovits. Cycles of even length in graphs.Journal of Combinatorial Theory, Series B, 16:97–105, 1974.

    Article  MATH  MathSciNet  Google Scholar 

  6. N. Chiba and L. Nishizeki. Arboricity and subgraph listing algorithms.SIAM Journal on Computing, 14:210–223, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  7. D. Eppstein. Subgraph isomorphism in planar graphs and related problems.Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA, pages 632–640, 1995.

  8. A. Itai and M. Rodeh. Finding a minimum circuit in a graph.SIAM Journal on Computing, 7:413–423, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  9. T. Kloks, D. Kratsch, and H. Müller. Finding and counting small induced subgraphs efficiently.Proceedings of the 21st International Workshop on Graph-Theoretic Concepts in Computer Science, Aachen, Lecture Notes in Computer Sciences Vol. 1017, pages 14–23. Springer-Verlag, 1995.

  10. D. W. Matula and L. L. Beck. Smallest-last ordering and clustering and graph coloring algorithms.Journal of the ACM, 30:417–427, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  11. B. Monien. How to find long paths efficiently.Annals of Discrete Mathematics, 25:239–254, 1985.

    MATH  MathSciNet  Google Scholar 

  12. J. Nešetřil and S. Poljak. On the complexity of the subgraph problem.Commentationes Mathematicae Universitatis Carolinae, 26(2):415–419, 1985.

    MathSciNet  Google Scholar 

  13. C. H. Papadimitriou and M. Yannakakis. The clique problem for planar graphs.Information Processing Letters, 13:131–133, 1981.

    Article  MathSciNet  Google Scholar 

  14. D. Richards. Finding short cycles in a planar graph using separators.Journal of Algorithms, 7:382–394, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  15. G. Sundaram and S. S. Skiena. Recognizing small subgraphs.Networks, 25:183–191, 1995.

    MATH  MathSciNet  Google Scholar 

  16. R. Yuster and U. Zwick. Finding even cycles even faster.Proceedings of the 21st International Colloquium on Automata, Languages and Programming, Jerusalem, Lecture Notes in Computer Science, Vol. 820, pages 532–543, Springer-Verlag, Berlin, 1994. Journal version to appear inSIAM Journal on Discrete Mathematics.

    Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    N. Alon, R. Yuster & U. Zwick

Authors
  1. N. Alon
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  2. R. Yuster
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  3. U. Zwick
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Additional information

Communicated by N. Megiddo.

This work was supported in part by The Basic Research Foundation administrated by The Israel Academy of Sciences and Humanities.

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Alon, N., Yuster, R. & Zwick, U. Finding and counting given length cycles. Algorithmica 17, 209–223 (1997). https://doi.org/10.1007/BF02523189

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  • DOI: https://doi.org/10.1007/BF02523189

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