Problems and results in extremal combinatorics—II

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 [N. Alon, Problems and results in extremal combinatorics—I, Discrete Math. 273 (2003), 31–53.] of the same flavor, and hopefully a predecessor of another related future paper. Each section of this paper is essentially self contained, and can be read separately.