A short proof of w1n (Hom(C2r+1, Kn+2)) = 0 for all n and A graph colouring theorem by Babson and Kozlov
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We show that the n-th power of the first Stiefel-Whitney class of the ℤ2-action on the graph complex Hom(C2r+1, Kn+2) is zero, confirming a conjecture by Babson and Kozlov. This yields a considerably simplified proof of their graph colouring theorem, which is also known as the Lovsz conjecture.
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