Skip to main content
SpringerLink
Log in

Reflections on a Problem of Erdős and Hajnal

  • Chapter
  • First Online:
The Mathematics of Paul Erdős II

Summary

We consider some problems suggested by special cases of a conjecture of Erdős and Hajnal.

Supported by OTKA grant 2570.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

Bibliography

  1. C. Berge, D. Duchet, Strongly perfect graphs, in Topics on Perfect graphs, Annals of Discrete Math. Vol 21 (1984) 57–61.

    MathSciNet  Google Scholar 

  2. Z. Blázsik, M. Hujter, A. Pluhár, Zs. Tuza, Graphs with no induced C 4 and 2K 2, Discrete Math. 115 (1993) 51–55.

    Google Scholar 

  3. F. R. K. Chung, On the covering of graphs, Discrete Math. 30 (1980) 89–93.

    Article  MathSciNet  MATH  Google Scholar 

  4. P. Erdős, Graph Theory and Probability II., Canadian J. Math. 13, (1961) 346–352.

    Article  Google Scholar 

  5. P. Erdős, Some Remarks on the Theory of Graphs, Bulletin of the American Mathematics Society, 53 (1947), 292–294.

    Article  Google Scholar 

  6. P. Erdős, A. Gyárfás, T. Łuczak, Graphs in which each C 4 spans K 4, Discrete Math. 154 (1996) 263–268.

    Article  MathSciNet  Google Scholar 

  7. P. Erdős, A. Hajnal, Ramsey Type Theorems, Discrete Applied Math. 25 (1989) 37–52.

    Article  Google Scholar 

  8. J. L. Fouquet, A decomposition for a class of \((P_{5},\overline{P_{5}})\)-free graphs, Discrete Math. 121 (1993) 75–83.

    Article  MathSciNet  MATH  Google Scholar 

  9. A. Gyárfás, A Ramsey type Theorem and its applications to relatives of Helly’s theorem, Periodica Math. Hung. 3 (1973) 299–304.

    Article  MATH  Google Scholar 

  10. A. Gyárfás, Problems from the world surrounding perfect graphs, Zastowania Matematyki, Applicationes Mathematicae, XIX 3–4 (1987) 413–441.

    Google Scholar 

  11. Hirschfeld, Finite Projective Spaces of three dimensions, Clarendon Press, Oxford, 1985.

    Google Scholar 

  12. L. Lovász, Perfect Graphs, in Selected Topics in Graph Theory 2. Academic Press (1983) 55–87.

    Google Scholar 

  13. H. J. Prömel, A.Steger, Almost all Berge graphs are perfect, Combin. Probab. Comput. 1 (1992) 53–79.

    Article  MathSciNet  MATH  Google Scholar 

  14. D. Seinsche, On a property of the class of n-colorable graphs, Journal of Combinatorial Theory B. 16 (1974) 191–193.

    Article  MathSciNet  MATH  Google Scholar 

  15. J. Spencer, Ten lectures on the Probabilistic method, CBMS-NSF Conference Series, 52.

    Google Scholar 

  16. S. Wagon, A bound on the chromatic number of graphs without certain induced subgraphs, J. Combinatorial Theory B. 29 (1980) 345–346.

    Article  MathSciNet  MATH  Google Scholar 

  17. N. Alon, J. Pach, J. Solymosi, Ramsey-type theorems with forbidden subgraphs, Combinatorica 21 (2001) 155–170.

    Article  MathSciNet  MATH  Google Scholar 

  18. M. Chudnovsky, N. Robertson, P. Seymour, R. Thomas, The strong perfect graph theorem, Annals of Math. 164 (2006) 51–229.

    Article  MathSciNet  MATH  Google Scholar 

  19. M. Chudnovsky, S. Safra, The Erdős-Hajnal conjecture for bull-free graphs, J. Combinatorial Theory B, 98 (2008) 1301–1310.

    Article  MathSciNet  MATH  Google Scholar 

  20. M. Chudnovsky, P. Seymour, Excluding paths and antipaths, submitted manuscript.

    Google Scholar 

  21. M. Chudnovsky, Y. Zwols, Large cliques or stable sets in graphs with no four-edge path and no five-edge path in the complement, Journal of Graph Theory, DOI 10.1002/jgt.20626

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Alfrd Rnyi Institute of Mathematics, Hungarian Academy of Sciences, 127, H-1364, Budapest, Hungary

    András Gyárfás

Authors
  1. András Gyárfás
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to András Gyárfás .

Editor information

Editors and Affiliations

  1. Dept. Comp. Sci. & Engineering, University of California, San Diego, La Jolla, California, USA

    Ronald L. Graham

  2. Department of Applied Mathematics, Charles University Department of Applied Mathematics, Prague, Czech Republic

    Jaroslav Nešetřil

  3. Department of Mathematics, Iowa State University, Ames, Iowa, USA

    Steve Butler

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Gyárfás, A. (2013). Reflections on a Problem of Erdős and Hajnal. In: Graham, R., Nešetřil, J., Butler, S. (eds) The Mathematics of Paul Erdős II. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7254-4_11

Download citation

Publish with us

Policies and ethics

Search

Navigation