We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
BLOCK COLOURINGS OF 6-CYCLE SYSTEMS.
- Authors
Bonacini, Paola; Gionfriddo, Mario; Marino, Lucia
- 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.
- Subjects
GEOMETRIC vertices; STEINER systems; BLOCK designs; COMBINATORIAL designs &; configurations; COMBINATORICS
- Publication
Opuscula Mathematica, 2017, Vol 37, Issue 5, p647
- ISSN
1232-9274
- Publication type
Article
- DOI
10.7494/OpMath.2017.37.5.647