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 = 3 mod 6 and at
most (v+5)/2 when v = 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 = 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 = 15 mod 18 that there are
at least vv2(1/6+o(1)) non-isomorphic Steiner
triple systems with chromatic index at least (v+3)/2 and that some of
these systems are cyclic.