Algebraic Graph Theory

    Paper details: 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 1. How is the f the same thing as a fractional colouring ? Create an example for that 2. Proof Theorem 7.3.2 (very important !) 3. Proof Lemma 7.3.1