  We show that the n-th power of the first Stiefel-Whitney class of the
Z_2-operation on the graph complex Hom(C_{2r+1},K_{n+2})$ is zero, confirming a
conjecture by Babson and Kozlov. This proves the strong form of their graph
colouring theorem, which they had only proven for odd n. Our proof is also
considerably simpler than their proof of the weak form of the theorem, which is
also known as the Lov\'asz conjecture.
