The erdős existence argument

Joel Spencer

doi:10.1007/978-1-4614-7258-2_27

The erdős existence argument

Joel Spencer

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

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 (Electronic)	9781461472582
ISBN (Print)	9781461472575
DOIs	https://doi.org/10.1007/978-1-4614-7258-2_27
State	Published - Jan 1 2013

ASJC Scopus subject areas

General Mathematics

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

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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 Erd{\H o}s. Here we reexamine some of his critical early papers. We begin, as all with knowledge of the field would expect, with the 1947 paper Erd{\H o}s 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 Erd{\H o}s{\textquoteright}s overall mathematical publications) and our remaining papers all were published in a single ten year span from 1955 to 1965.",

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The erdős existence argument

Abstract

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