Colour the remaining (greedily colourable) graph in (of course) a greedy manner.
This can easily be achieved by a simple greedy strategy.
This is to be expected as he proves his lower bound via the analysis of a greedy algorithm.
We actually prove limit theorems (central limit theorem and large deviation principle) on the number of phases of this greedy algorithm.
In this section we discuss only the case relevant to the use of nonlinear approximation, in particular, greedy approximation in such a construction.
In this survey we discuss properties of specific methods of approximation that belong to a family of greedy approximation methods (greedy algorithms).
The needs of nonlinear approximation, or, more specifically, the needs of greedy approximation lead us to new concepts of bases: greedy bases and quasi-greedy bases.
There are no books on greedy approximation at present.
