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Problems and results in Extremal Combinatorics-II Dedicated to Miki Simonovits, for his 60th-birthday

Summary: Problems and results in Extremal Combinatorics- II
Noga Alon
Dedicated to Miki Simonovits, for his 60th-birthday
Extremal Combinatorics is one of the central areas in Discrete Mathematics. It deals with
problems that are often motivated by questions arising 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, Polyhedral
Combinatorics and Probabilistic Combinatorics. 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 biased, and as the title of the paper suggests, it is a
sequel to a previous paper [2] of the same flavour, and hopefully a predecessor of another related
future paper. 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 value of an invariant of a combinatorial object that satisfies certain requirements.
Problems of this type are often related to other areas including Computer Science, Information The-
ory, Number Theory and Game Theory. This branch of Combinatorics has been very active during
the last few decades, see, e.g., [5], [10], and their many references.


Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University


Collections: Mathematics