Steiner triple systems with high chromatic index
| Autor: | Daniel Horsley, Charles J. Colbourn, Darryn Bryant, Ian M. Wanless |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Sublinear function
General Mathematics Order (ring theory) 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology Disjoint sets 05B07 (Primary) 05C15 (Secondary) 01 natural sciences Combinatorics Edge coloring Steiner system Integer 010201 computation theory & mathematics 0202 electrical engineering electronic engineering information engineering FOS: Mathematics Mathematics - Combinatorics Combinatorics (math.CO) Mathematics |
| DOI: | 10.48550/arxiv.1702.00521 |
| Popis: | It is conjectured that every Steiner triple system of order $v \neq 7$ has chromatic index at most $(v+3)/2$ when $v \equiv 3 \pmod{6}$ and at most $(v+5)/2$ when $v \equiv 1 \pmod{6}$. Herein, we construct a Steiner triple system of order $v$ with chromatic index at least $(v+3)/2$ for each integer $v \equiv 3 \pmod{6}$ such that $v \geq 15$, 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 $v \equiv 15 \pmod{18}$ 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. Comment: 10 pages, 0 figures |
| Databáze: | OpenAIRE |
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