Journal of Combinatorics

Volume 7 (2016)

Number 2–3

Guest editors: Rong Luo and Cun-Quan Zhang

Problems and results in Extremal Combinatorics – III

Pages: 233 – 256

DOI: http://dx.doi.org/10.4310/JOC.2016.v7.n2.a2

Author

Noga Alon (Sackler School of Mathematics and Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv, Israel; and School of Mathematics, Institute for Advanced Study, Princeton, New Jersey, U.S.A.)

Abstract

Extremal Combinatorics is one of the most active topics in Discrete Mathematics, dealing with problems that are often motivated by questions in other areas, including Theoretical Computer Science, Geometry and Game Theory. This paper contains a collection of problems and results in the area, including solutions or partial solutions to open problems suggested by various researchers. The topics considered here include questions in Extremal Graph Theory, Combinatorial Geometry and Combinatorial Number Theory. This is not a comprehensive survey of the area, and is merely a collection of various extremal problems, which are hopefully interesting. The choice of the problems is inevitably biased, and as the title of the paper suggests, it is a sequel of two previous papers of the same flavour. Each section of this paper is essentially self-contained, and can be read separately.

Keywords

tournament, homometric sets in graphs, Steiner systems, list coloring, sign matrices

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