due Nov 9

1.  Write an ILP to express the graph colouring problem.  You should
    minimize the number of colours needed.  Hint: Use indicator
    variables x_{vi} which should take value 1 if vertex v gets colour
    i.  

    Expressing a problem as an ILP is an important skill; even though
    best algorithms for ILPs take exponential time in general, for
    small problems this may be a very quick, easy way to get optimal
    solutions.

2.  Solve problem 1 from the notes on 3Sat.  

3.  Solve problem 4 from the notes on 3Sat.  

4.  Solve exercise 13.1 of KT.