Skip to main content

The Erdős Existence Argument

  • Chapter
  • First Online:
The Mathematics of Paul Erdős I
  • 2225 Accesses

Summary

The Probabilistic Method is now a standard tool in the combinatorial toolbox but such was not always the case. The development of this methodology was for many years nearly entirely due to one man: Paul Erdős. Here we reexamine some of his critical early papers. We begin, as all with knowledge of the field would expect, with the 1947 paper Erdős P (1947) Some remarks on the theory of graphs. Bull Amer Math Soc 53:292–294 giving a lower bound on the Ramsey function R(k, k). There is then a curious gap (certainly not reflected in Erdős’s overall mathematical publications) and our remaining papers all were published in a single ten year span from 1955 to 1965.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

Similar content being viewed by others

References

  1. P. Erdős, Problems and results in additive number theory, in Colloque sur la Théorie des Nombres (CBRM), Bruxelles, 1955, 127–137.

    Google Scholar 

  2. P. Erdős, Graph Theory and Probability, Canad. J. Math. 11 (1959), 34–38.

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  4. P. Erdős, On circuits and subgraphs of chromatic graphs, Mathematika 9(1962), 170–175.

    Article  MathSciNet  Google Scholar 

  5. P. Erdős, On a combinatorial problem I., Nordisk. Mat. Tidskr. 11 (1963), 5–10.

    Google Scholar 

  6. P. Erdős, On a combinatorial problem II., Acta. Math. Acad. Sci. Hungar. 15 (1964), 445–447.

    Google Scholar 

  7. P. Erdős and J. W. Moon, On sets of consistent arcs in a tournament, Canad. Math. Bull. 8 (1965), 269–271.

    Article  MathSciNet  Google Scholar 

  8. P. Erdős and A. Rényi, On the evolution of random graphs, Mat. Kutató Int. Közl. 5 (1960), 17–60.

    Google Scholar 

  9. P. Erdős and J. Spencer, Imbalances in k-colorations, Networks 1 (1972), 379–385.

    Article  Google Scholar 

  10. P. Erdős and G. Szekeres, A combinatorial problem in geometry, Compositio Math. 2 (1935), 463–470.

    MathSciNet  Google Scholar 

  11. W. F. de la Vega, On the maximal cardinality of a consistent set of arcs in a random tournament, J. Combinatorial Theory, Series B 35 (1983), 328–332.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Joel Spencer .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Spencer, J. (2013). The Erdős Existence Argument. In: Graham, R., Nešetřil, J., Butler, S. (eds) The Mathematics of Paul Erdős I. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7258-2_27

Download citation

Publish with us

Policies and ethics