The chromatic number of the kneser graphs

Book: Algebraic Graph Theory written by Chris Godsil, Gordon Royle, chapter 7 Kneser Graphs.
The task is the following:
Work out the pages 136-138 . These are the topics and the questions to be solved:
7.2 Fractional cliques:

1. Why is w*(x) greater than w(x) ?
2. Why is g a fractional clique ?
3. Proof Lemma 7.2.1
4. Proof of Lemma 7.2.2 : If X is vertex transitive, why is then g^ constant on the vertices of X ? Why is c1 a fractional clique ?
5. How does the result follow ?
   7.3 Fractional chromatic number
6. How is the f the same thing as a fractional colouring ? Create an example for that
7. Proof Theorem 7.3.2 (very important !)
8. Proof Lemma 7.3.1

Sample Solution