The main purpose of this lecture is to show that if one picks a

forbidden graph

or quasi-asymptotic results provide almost immediate solution

of the corresponding Turán type extremal problem.

Among others, I shall "determine" the Turán extremal number of the

Petersen graph. We shall prove, e.g., that for

extremal graph for the Petersen graph

on

other and to all the vertices of

The solutions of the problems discussed in the lecture will lead to

some general theorems.

One case discussed by me is an old theorem, back from 1974, on extremal problems where the decomposition class contains a path.