Skip to main content

A Note on k-Colorability of P 5-Free Graphs

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5162))

Abstract

We present a polynomial-time algorithm determining whether or not, for a fixed k, a P 5-free graph can be k-colored. If such a coloring exists, the algorithm will produce one.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ramirez Alfonsin, J.L., Reed, B.A.: Perfect Graphs. John Wiley & Sons, LTD, Chichester (2001)

    MATH  Google Scholar 

  2. Bacsó, G., Tuza, Z.: Dominating cliques in P 5-free graphs. Period. Math. Hungar. 21(4), 303–308 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  3. Berge, C., Chvátal, V. (eds.): Topics on perfect graphs. North-Holland, Amsterdam (1984)

    MATH  Google Scholar 

  4. Even, S., Pnueli, A., Lempel, A.: Permutation graphs and transitive graphs. J. Assoc. Comput. Mach. 19, 400–410 (1972)

    MATH  MathSciNet  Google Scholar 

  5. Garey, M.R., Johnson, D.S., Stockmeyer, L.: Some simplified NP-complete problems. Theoretical Computer Science 1, 237–267 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  6. Gavril, F.: Algorithms for minimum coloring, maximum clique, minimum coloring by cliques, and maximum independent set of a chordal graph. SIAM J. Comput. 1, 180–187 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  7. Golumbic, M.C.: Algorithmic graph theory and perfect graphs. Academic Press, New York (1980)

    MATH  Google Scholar 

  8. Grötschel, M., Lovász, L., Schrjver, A.: The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1, 169–197 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  9. Hayward, R., Hoàng, C.T., Maffray, F.: Optimizing weakly triangulated graphs. Graphs and Combinatorics 5, 339–349 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  10. Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum Press, New York (1972)

    Google Scholar 

  11. Kral, D., Kratochvil, J., Tuza, Z., Woeginger, G.J.: Complexity of Coloring Graphs without Forbidden Induced Subgraphs. In: Brandstädt, A., Van Le, B. (eds.) WG 2001. LNCS, vol. 2204, pp. 254–262. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  12. Le, V.B., Randerath, B., Schiermeyer, I.: On the complexity of 4-coloring graphs without long induced paths. Theoretical Computer Science 389(1-2), 330–335 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  13. Randerath, B., Schiermeyer, I.: 3-Colorability ∈ P for P 6-free graphs. Discrete Applied Mathematics 136(2-3), 299–313 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  14. Sgall, J., Woeginger, G.J.: The complexity of coloring graphs without long induced paths. Acta Cybernet 15(1), 107–117 (2001)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Edward Ochmański Jerzy Tyszkiewicz

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hoàng, C.T., Kamiński, M., Lozin, V., Sawada, J., Shu, X. (2008). A Note on k-Colorability of P 5-Free Graphs. In: Ochmański, E., Tyszkiewicz, J. (eds) Mathematical Foundations of Computer Science 2008. MFCS 2008. Lecture Notes in Computer Science, vol 5162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85238-4_31

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-85238-4_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85237-7

  • Online ISBN: 978-3-540-85238-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics