STEINER TRIPLE SYSTEMS WITH HIGH CHROMATIC INDEX

It has been conjectured that every Steiner triple system of order v + 7 has chromatic index at most (v + 3)/2 when v equivalent to 3 (mod 6) and at most (v + 5)/2 when v equivalent to 1 (mod 6). Herein, we construct a Steiner triple system of order v with chromatic index at least (v + 3)/2 for each integer v equivalent to 3 (mod 6) such that v >= 15, with four possible exceptions. We further show that the maximum number of disjoint parallel classes in the systems constructed is sublinear in v. Finally, we establish for each order v equivalent to 15 (mod 18) that there are at least v(v2(1/6+0(1))) nonisomorphic Steiner triple systems with chromatic index at least (v + 3)/2 and that some of these systems are cyclic.