 
Summary: Extremal and Probabilistic
Combinatorics
N. Alon and M. Krivelevich Revised, August
2006
Sackler Faculty of Exact Sciences, Tel Aviv
University, Tel Aviv, Israel 69978
1 Combinatorics an introduction
1.1 Examples
It is hard to give a rigorous definition of Combi
natorics, hence we start with a few examples il
lustrating the area. Testing friendship relations
between children some fifty years ago, the Hungar
ian sociologist S. Szalai observed that any group of
about twenty children he checked contained a set
of four children any two of whom were friends, or
a set of four no two of whom were friends. De
spite the temptation to try and draw some behav
ioral consequences, Szalai realized this may well
be a mathematical phenomenon, rather than a so
ciological one. Indeed, a brief discussion with the
