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Erdős Centennial pp 535–583Cite as

Extremal Results in Random Graphs

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Part of the book series: Bolyai Society Mathematical Studies ((BSMS,volume 25))

Abstract

According to Paul Erdős au][Some notes on Turán’s mathematical work, J. Approx. Theory 29 (1980), page 4]_it was Paul Turán who “created the area of extremal problems in graph theory”. However, without a doubt, Paul Erdős popularized extremal combinatorics, by his many contributions to the field, his numerous questions and conjectures, and his influence on discrete mathematicians in Hungary and all over the world. In fact, most of the early contributions in this field can be traced back to Paul Erdős, Paul Turán, as well as their collaborators and students. Paul Erdős also established the probabilistic method in discrete mathematics, and in collaboration with Alfréd Rényi, he started the systematic study of random graphs. We shall survey recent developments at the interface of extremal combinatorics and random graph theory.

First author was supported by NSF grant DMS 0800070.

Second author was supported through the Heisenberg-Programme of the Deutsche Forschungsgemeinschaft (DFG Grant SCHA 1263/4-1).

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  1. Department of Mathematics and Computer Science, Emory University, Atlanta, GA, 30322, USA

    Vojtěch Rödl

  2. Fachbereich Mathematik, Universität Hamburg, Bundesstraße 55, D-20146, Hamburg, Germany

    Mathias Schacht

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  1. Department of Computer Science, Eötvös Lóránd University, Pázmány P. sétány 1/c, Budapest, 1117, Hungary

    László Lovász

  2. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13–15, Budapest, 1053, Hungary

    Imre Z. Ruzsa  & Vera T. Sós  & 

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Dedicated to the memory of Paul Erdős on the occasion of his 100th birthday

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Rödl, V., Schacht, M. (2013). Extremal Results in Random Graphs. In: Lovász, L., Ruzsa, I.Z., Sós, V.T. (eds) Erdős Centennial. Bolyai Society Mathematical Studies, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39286-3_20

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