Equitable edge coloured Steiner triple systems

A k-edge coloring of G is said to be equitable if the number of edges, at any vertex, colored with a certain color differ by at most one from the number of edges colored with a different color at the same vertex. An STS(v) is said to be polychromatic if the edges in each triple are colored with three different colors. In this paper, we show that every STS(v) admits a 3-edge coloring that is both polychromatic for the STS(v) and equitable for the underlying complete graph. Also, we show that, for v ≡ 1 or 3 (mod 6), there exists an equitable k-edge coloring of Kv which does not admit any polychromatic STS(v), for k = 3 and k = v − 2.