### Abstract

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.

Original language | English (US) |
---|---|

Title of host publication | The Mathematics of Paul Erdos I, Second Edition |

Publisher | Springer New York |

Pages | 435-444 |

Number of pages | 10 |

ISBN (Print) | 9781461472582, 9781461472575 |

DOIs | |

State | Published - Jan 1 2013 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*The Mathematics of Paul Erdos I, Second Edition*(pp. 435-444). Springer New York. https://doi.org/10.1007/978-1-4614-7258-2_27

**The erdős existence argument.** / Spencer, Joel.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*The Mathematics of Paul Erdos I, Second Edition.*Springer New York, pp. 435-444. https://doi.org/10.1007/978-1-4614-7258-2_27

}

TY - CHAP

T1 - The erdős existence argument

AU - Spencer, Joel

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84956687806&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84956687806&partnerID=8YFLogxK

U2 - 10.1007/978-1-4614-7258-2_27

DO - 10.1007/978-1-4614-7258-2_27

M3 - Chapter

AN - SCOPUS:84956687806

SN - 9781461472582

SN - 9781461472575

SP - 435

EP - 444

BT - The Mathematics of Paul Erdos I, Second Edition

PB - Springer New York

ER -