On the Block Coloring of Steiner Triple Systems

A Steiner triple system of order v, STS(v), is an ordered pair S = (V,B), where V is a set of size v and B is a collection of triples of V such that every pair of V is contained in exactly one triple of B. A k-block coloring is a partitioning of the set B into k color classes such that every two blocks in one color class do not intersect. In this paper, we introduce a construction and use it to show that for every k-block colorable STS(v) and l-block colorable STS(w), there exists a (k+lv)-block colorable STS(vw). Moreover, it is shown that for every kblock colorable STS(v), every STS(2v+1) obtained from the well-known construction is (k + v)-block colorable.