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Certifying Algorithms for Recognizing Proper Circular-Arc Graphs and Unit Circular-Arc Graphs

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Graph-Theoretic Concepts in Computer Science (WG 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4271))

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Abstract

We give two new algorithms for recognizing proper circular-arc graphs and unit circular-arc graphs. The algorithms either provide a model for the input graph, or a certificate that proves that such a model does not exist and can be authenticated in O(n) time.

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References

  1. Deng, X., Hell, P., Huang, J.: Linear-time representation algorithms for proper circular-arc graphs and proper interval graphs. SIAM J. Comput. 25(2), 390–403 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  2. Durán, G., Gravano, A., McConnell, R.M., Spinrad, J.P., Tucker, A.: Polynomial time recognition of unit circular-arc graphs. J. Algorithms 58(1), 67–78 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  3. Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs. Academic Press, London (1980)

    MATH  Google Scholar 

  4. Hell, P., Huang, J.: Certifying LexBFS recognition algorithms for proper interval graphs and proper interval bigraphs. SIAM J. Discrete Math. 18(3), 554–570 (2004)

    Article  MathSciNet  Google Scholar 

  5. Hell, P., Huang, J.: Interval bigraphs and circular arc graphs. J. Graph Theory 46(4), 313–327 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kaplan, H., Nussbaum, Y.: A simpler linear-time recognition of circular-arc graphs. In: Arge, L., Freivalds, R. (eds.) SWAT 2006. LNCS, vol. 4059, pp. 41–52. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Kratsch, D., McConnell, R.M., Mehlhorn, K., Spinrad, J.P.: Certifying algorithms for recognizing interval graphs and permutation graphs. SIAM J. Comput. 36(2), 326–353 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  8. Lin, M.C., Szwarcfiter, J.L.: Efficient construction of unit circular-arc models. In: SODA 2006: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm, pp. 309–315 (2006)

    Google Scholar 

  9. McConnell, R.M.: Linear-time recognition of circular-arc graphs. Algorithmica 37(2), 93–147 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  10. McConnell, R.M.: A certifying algorithm for the consecutive-ones property. In: SODA 2004: Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms, pp. 768–777 (2004)

    Google Scholar 

  11. Mehlhorn, K., Näeher, S.: The LEDA Platform for combinatorial and geometric computing. Cambridge University Press, Cambridge (1999)

    Google Scholar 

  12. Meister, D.: Recognition and computation of minimal triangulations for AT-free claw-free and co-comparability graphs. Discrete Applied Math. 146(3), 193–218 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  13. Skrien, D.J.: A relationship between triangulated graphs, comparability graphs, proper interval graphs, proper circular-arc graphs, and nested interval graphs. J. Graph Theory 6, 309–316 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  14. Spinrad, J.P.: Efficient Graph Representations. Fields Institute Monographs, vol. 19. American Mathematical Society (2003)

    Google Scholar 

  15. Tarjan, R.E., Yannakakis, M.: Addendum: Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM J. Comput. 14(1), 254–255 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  16. Tucker, A.: Matrix characterizations of circular-arc graphs. Pacific J. Math. 39(2), 535–545 (1971)

    MATH  MathSciNet  Google Scholar 

  17. Tucker, A.: Structure theorems for some classes of circular-arc graphs. Discrete Math. 7, 167–195 (1974)

    Article  MATH  MathSciNet  Google Scholar 

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© 2006 Springer-Verlag Berlin Heidelberg

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Kaplan, H., Nussbaum, Y. (2006). Certifying Algorithms for Recognizing Proper Circular-Arc Graphs and Unit Circular-Arc Graphs. In: Fomin, F.V. (eds) Graph-Theoretic Concepts in Computer Science. WG 2006. Lecture Notes in Computer Science, vol 4271. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11917496_26

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  • DOI: https://doi.org/10.1007/11917496_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-48381-6

  • Online ISBN: 978-3-540-48382-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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