 
Summary: Problems and results in Extremal Combinatorics, Part I
Noga Alon
Abstract
Extremal Combinatorics is an area in Discrete Mathematics that has developed spectacularly
during the last decades. This paper contains a collection of problems and results in the area,
including solutions or partial solutions to open problems suggested by various researchers in
Extremal Graph Theory, Extremal Finite Set Theory and Combinatorial Geometry. This is not
meant to be a comprehensive survey of the area, it is merely a collection of various extremal
problems, which are hopefully interesting. The choice of the problems is inevitably somewhat
biased, and as the title of the paper suggests I hope to write a related paper in the future. Each
section of this paper is essentially self contained, and can be read separately.
1 Introduction
Extremal Combinatorics deals with the problem of determining or estimating the maximum or min
imum possible cardinality of a collection of finite objects that satisfies certain requirements. Such
problems are often related to other areas including Computer Science, Information Theory, Number
Theory and Geometry. This branch of Combinatorics has developed spectacularly over the last few
decades, see, e.g., [10], [31], and their many references.
This paper contains a collection of problems and results in the area, including solutions or partial
solutions to open problems suggested by various researchers in Extremal Graph Theory, Extremal
Finite Set Theory and Combinatorial Geometry. This is not meant to be a comprehensive survey of
