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BLOCK COLOURINGS OF 6-CYCLE SYSTEMS.
- Source :
-
Opuscula Mathematica . 2017, Vol. 37 Issue 5, p647-664. 18p. - Publication Year :
- 2017
-
Abstract
- Let Σ = (X, B) be a 6-cycle system of order v, so v = 1, 9 mod 12. A c-colouring of type s is a map φ B → C, with C set of colours, such that exactly c colours are used and for every vertex x all the blocks containing x are coloured exactly with s colours. Let v-1/2 = qs + r, with q, r ≥ 0. φ is equitable if for every vertex x the set of the v-1/2 blocks containing x is partitioned in r colour classes of cardinality q + 1 and s - r colour classes of cardinality q. In this paper we study bicolourings and tricolourings, for which, respectively, s = 2 and s = 3, distinguishing the cases v = 12k+1 and v = 12k+9. In particular, we settle completely the case of s = 2, while for s = 3 we determine upper and lower bounds for c. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 12329274
- Volume :
- 37
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Opuscula Mathematica
- Publication Type :
- Academic Journal
- Accession number :
- 125415046
- Full Text :
- https://doi.org/10.7494/OpMath.2017.37.5.647