Steiner triple systems with high chromatic index release_pqvlrgc63bhjtfhersqxrekpbq

by Darryn Bryant, Charles Colbourn, Daniel Horsley, Ian M. Wanless

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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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Date   2017-07-27
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arXiv  1702.00521v3
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