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More Sets, Graphs and Numbers pp 199–262Cite as

Pseudo-random Graphs

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Part of the book series: Bolyai Society Mathematical Studies ((BSMS,volume 15))

Abstract

Random graphs have proven to be one of the most important and fruitful concepts in modern Combinatorics and Theoretical Computer Science. Besides being a fascinating study subject for their own sake, they serve as essential instruments in proving an enormous number of combinatorial statements, making their role quite hard to overestimate. Their tremendous success serves as a natural motivation for the following very general and deep informal questions: what are the essential properties of random graphs? How can one tell when a given graph behaves like a random graph? How to create deterministically graphs that look random-like? This leads us to a concept of pseudo-random graphs.

Research supported in part by a USA-Israel BSF Grant, by a grant from the Israel Science Foundation and by a Bergmann Memorial Grant.

Research supported in part by NSF grants DMS-0355497, DMS-0106589, and by an Alfred P. Sloan fellowship. Part of this research was done while visiting Microsoft Research.

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Authors and Affiliations

  1. Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, 69978, Israel

    Michael Krivelevich

  2. Department of Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Benny Sudakov

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  1. Michael Krivelevich
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  2. Benny Sudakov
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Editors and Affiliations

  1. Hungarian Academy of Sciences, Alfréd Rényi Inst. of Mathematics, Reáltanoda u. 13-15, 1053, Budapest, Hungary

    Ervin Győri  & Gyula O. H. Katona  & 

  2. Eötvös University (Budapest)/Microsoft (Seattle), Pázmány Péter sétány 1/C, 1117, Budapest, Hungary

    László Lovász

  3. Budapest University of Technology and Economics, Pázmány Péter sétány 1/D, 1117, Budapest, Hungary

    Tamás Fleiner

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© 2006 János Bolyai Mathematical Society and Springer Verlag

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Krivelevich, M., Sudakov, B. (2006). Pseudo-random Graphs. In: Győri, E., Katona, G.O.H., Lovász, L., Fleiner, T. (eds) More Sets, Graphs and Numbers. Bolyai Society Mathematical Studies, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32439-3_10

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