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

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

Collections: Mathematics