Skip to main content

The chromatic number of triangle-free graphs

Part of the Lecture Notes in Mathematics book series (LNM,volume 303)

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • 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

References

  1. V. Chvátal, The smallest triangle-free 4-chromatic 4-regular graph, J. Combinatorial Theory 9 (1970), 93–94.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. B. Descartes (pseudonym of Tutte), A three color problem, Eureka (April 1947); Solution (March 1948).

    Google Scholar 

  3. G. Dirac, A theorem of R. L. Brooks and a conjecture of H. Hadwiger, Proc. London Math. Soc. (3) 7 (1957), 161–195.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. P. Erdös, Graph theory and probability, Canad. J. Math. 11 (1959), 34–38.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. B. Grötzsch, Ein Driefarbensatz für dreikreisfreie Netze auf der Kugel, Wiss. Z. Martin — Luther Univ., Halle-Wittenberg, Math. Nat. Reihe 8 (1958.59), 109–120.

    Google Scholar 

  6. F. Harary, Graph Theory, Addison-Wesley, Reading, Mass., 1969.

    MATH  Google Scholar 

  7. H. Kronk and A. white, A 4-color theorem for toroidal graphs, Proc. Amer. Math. Soc., to appear.

    Google Scholar 

  8. J. Mycielski, Sur le coloriage des graphs, Colloq. Math. 3 (1955), 161–162.

    MathSciNet  MATH  Google Scholar 

  9. A. A. Zykov, On some properties of linear complexes, Math. Sb. 24 (1949), 163–188.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1972 Springer-Verlag

About this paper

Cite this paper

Kronk, H.V. (1972). The chromatic number of triangle-free graphs. In: Alavi, Y., Lick, D.R., White, A.T. (eds) Graph Theory and Applications. Lecture Notes in Mathematics, vol 303. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067369

Download citation

  • DOI: https://doi.org/10.1007/BFb0067369

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06096-3

  • Online ISBN: 978-3-540-38114-3

  • eBook Packages: Springer Book Archive