Coloring Steiner Triple Systems

In this paper, several results on the chromatic number of Steiner triple systems are established. A Steiner triple system is a simple 3-uniform hypergraph in which every pair of vertices is connected by exactly one 3-edge. Among other things, we prove that for any $k\geqq 3$ there exists an $n_k $ such that for all admissible $v \geqq n_k $ there exists a k-chromatic Steiner triple systems of order v. In addition we prove that for all $v \geqq 49$ there exists a 4-chromatic Steiner triple system of order v. An estimate of $n_k $ is also established, namely, $c_1 k^2 \log k > n_k > c_2 k^2 $.