Steiner triple systems with high chromatic index
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by
Darryn Bryant, Charles Colbourn, Daniel Horsley, Ian M. Wanless
2017
Abstract
It is conjectured that every Steiner triple system of order v ≠ 7 has
chromatic index at most (v+3)/2 when v ≡ 3 6 and at most
(v+5)/2 when v ≡ 1 6. Herein, we construct a Steiner triple
system of order v with chromatic index at least (v+3)/2 for each integer v
≡ 3 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 18 that there are at least v^v^2(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.
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