On the edge achromatic numbers of complete graphs

AbstractSuppose we wish to color the edges of the complete graph Kn with as many colors as possible so that (1) no two edges with a common node get the same color, and (2) for any two colors c1 and c2, there are two edges with a common node, one colored c1 and the other colored c2. What is the maximum number A(n) of colors possible in such a coloring? Coloring problems are notoriously hard and this problem is no exception. In fact, a remarkable theorem of André Bouchet implies that an exact determination of A(n) for all odd n would yield as a corollary all odd orders for which projective planes exist. Thus such a determination is clearly beyond the hopes of this study. The goals here are more modest: (1) to give a careful study of the best available upper bound on A(n), (2) to add to the constructions which give reasonable lower bounds for A(n), and (3) to contribute a few more values of n for which A(n) is known exactly