Hint for Homework 1, problem 3(b):

Suppose you're given an ordering for the vertices
of the k-by-k model problem.  Think of playing the
graph game in the given order, and consider the first 
time that you've either marked all the vertices in 
any single row or else marked all the vertices in 
any single column.  Show that, at that time, you 
have added edges to create a complete subgraph with
almost k vertices.

You may turn in any parts of problem 3 by the end
of the day Sunday, October 17, for half credit.  For 
each part of problem 3, I'll give you the larger of 
(full credit for what you turned in Friday) or (half
credit for what you turned in Sunday.)