Arc-transitive homogeneous factorizations and affine planes

We study arc-transitive homogeneous factorizations of a complete graph on 81 vertices and give an almost complete description of all possible factors that arise. In particular, we show that there exists an arc-transitive homogeneous factorization of K-81 such that the factors are isomorphic to the Hamming graph H(9, 2). This gives rise to an edge partition of K-81 into 90 copies of K-9 and it turns out that these copies of K9 form the blocks of the exceptional nearfield affine plane of order 9. (C) 2005 Wiley Periodicals. Inc.