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Almost Linear Time Computation of the Chromatic Polynomial of a Graph of Bounded Tree-Width

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LATIN 2010: Theoretical Informatics (LATIN 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6034))

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Abstract

An O(n log2 n) algorithm is presented to compute all coefficients of the chromatic polynomial of an n vertex graph of bounded tree-width. Previously, it has been known how to evaluate the chromatic polynomial for such graphs in linear time, implying a computation of all coefficients of the chromatic polynomial in quadratic time.

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References

  1. Birkhoff, B.D.: A determinant formula for the number of ways of coloring a map. Ann. of Math. 14, 42–46 (1912)

    Article  MathSciNet  Google Scholar 

  2. Biggs, N.: Algebraic graph theory, 2nd edn. Cambridge Mathematical Library. Cambridge University Press, Cambridge (1993)

    Google Scholar 

  3. Courcelle, B.: A multivariate interlace polynomial. CoRR abs/cs/0702016 (2007)

    Google Scholar 

  4. Makowsky, J.A.: From a zoo to a zoology: Towards a general theory of graph polynomials. Theor. Comp. Sys. 43(3), 542–562 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bläser, M., Hoffmann, C.: Fast evaluation of interlace polynomials on graphs of bounded treewidth. In: Fiat, A., Sanders, P. (eds.) ESA 2009. LNCS, vol. 5757, pp. 623–634. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  6. Makowsky, J.A., Mariño, J.P.: Farrell polynomials on graphs of bounded tree width. Advances in Applied Mathematics 30, 160–176 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Andrzejak, A.: An algorithm for the Tutte polynomials of graphs of bounded treewidth. Discrete Mathematics 190(1-3), 39–54 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  8. Noble, S.D.: Evaluating the Tutte polynomial for graphs of bounded tree-width. Combinatorics, Probability & Computing 7(3), 307–321 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  9. Makowsky, J.A., Rotics, U., Averbouch, I., Godlin, B.: Computing graph polynomials on graphs of bounded clique-width. In: Fomin, F.V. (ed.) WG 2006. LNCS, vol. 4271, pp. 191–204. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Fürer, M.: Efficient computation of the characteristic polynomial of a tree and related tasks. In: Fiat, A., Sanders, P. (eds.) ESA 2009. LNCS, vol. 5757, pp. 11–22. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  11. Bodlaender, H.L.: A linear time algorithm for finding tree-decompositions of small treewidth. SIAM Journal on Computing 25, 1305–1317 (1996)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Pennsylvania State University, University Park, PA, 16802, USA

    Martin Fürer

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  1. Martin Fürer
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Editors and Affiliations

  1. Faculty of Mathematics, Department of Computer Science, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Alejandro López-Ortiz

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Fürer, M. (2010). Almost Linear Time Computation of the Chromatic Polynomial of a Graph of Bounded Tree-Width. In: López-Ortiz, A. (eds) LATIN 2010: Theoretical Informatics. LATIN 2010. Lecture Notes in Computer Science, vol 6034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12200-2_6

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  • DOI: https://doi.org/10.1007/978-3-642-12200-2_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12199-9

  • Online ISBN: 978-3-642-12200-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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