Stiefel manifolds and coloring the pentagon

We prove Csorbaʼs conjecture that the Lovász complex Hom(C5,Kn) of graph multimorphisms from the 5-cycle C5 to the complete graph Kn is Z/2Z-equivariantly homeomorphic to the Stiefel manifold, Vn−1,2, the space of (ordered) orthonormal 2-frames in Rn−1.