Introduction to graph theory.
Bibliography (To be updated):
Graph Theory/ Reinhard Diestel. An online PDF copy can be found at
Diestel's website.
Lecture notes of Babai with proof of Matrix-Tree theorem
A paper by Gowers describing the connection between Szemeredi's Regularity Lemma
and Roth's theorem (see corollary 1.2) , and the generalization to 3-uniform hypergraphs
(see corollary 9.3) . A wonderfully written paper.
For more about Ramsey Theory see the book "Ramsey Theory" by Graham, Rothschild and Spencer.
A proof that R(3,k) is O(k^2/log(k)), taken from the book "The Probabilistic Method" by Alon
and Spencer.
The proof of the Shannon capacity of C_5 is taken from "Proofs from The Book",
but you may want to have a look at Lovasz' original paper, it is very readable.
A more comprehensive coverage of the various aspects of the Theta function
appears in the excellent survey paper of Knuth.
The paper covering the characterization of independent sets in products of K_3
(and other graphs)
Protocol/Syllabus
An evergrowing list of exercises
The format and content of the final exam