On cohomology groups of cycle graphs

In this thesis, especially some basic informations about Algeabric Topology is given for the problem determining the chromatic number of graphs. Pay using this information we examine proof of the Lovasz conjecture which states that if Hom(C2r+1, G) is k-connected, then χ(G) ≥ k + 4, where r, k є Z, r ≥ 1, k ≥ -1 and C2r+1 denotes the cycle with 2r+1 vertices. The proof requires analysis of Hom(C2r+1, Kn). The obstructions to graph colorings, for even n, by using structure of H*(Hom(C2r+1, Kn); Z) and for odd n, by using Stiefel-Whitney characteristic classes of Hom(C2r+1, Kn) are determined.