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Building Bridges II pp 1–16Cite as

Lovász, Vectors, Graphs and Codes

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Part of the book series: Bolyai Society Mathematical Studies ((BSMS,volume 28))

Abstract

A family of high-degree triangle-free pseudo-random Cayley graphs has been constructed in (Alon, Electro J Combin 1(R12):8, 1994 [2]), motivated by a geometric question of Lovász. These graphs turned out to be useful in tackling a variety of additional extremal problems in Graph Theory and Coding Theory. Here we describe the graphs and their applications, and mention several intriguing related open problems. This is mainly a survey, but it contains several new results as well. One of these is a construction showing that the Lovász \(\theta \)-function of a graph cannot be bounded by any function of its Shannon capacity.

Dedicated to László Lovász, for his seventieth birthday

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Acknowledgements

Research supported in part by NSF grant DMS-1855464, ISF grant 281/17, GIF grant G-1347-304.6/2016 and the Simons Foundation.

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Authors and Affiliations

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

    Noga Alon

  2. Schools of Mathematics and Computer Science, Tel Aviv University, 69978, Tel Aviv, Israel

    Noga Alon

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  1. Noga Alon
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Correspondence to Noga Alon .

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Editors and Affiliations

  1. MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    Imre Bárány

  2. MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    Gyula O. H. Katona

  3. MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    Attila Sali

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Alon, N. (2019). Lovász, Vectors, Graphs and Codes. In: Bárány, I., Katona, G., Sali, A. (eds) Building Bridges II. Bolyai Society Mathematical Studies, vol 28. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-59204-5_1

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