Colbourn, C.J., K.T. Phelps, M.J. de Resmini and A. Rosa, Partitioning Steiner triple systems into complete arcs, Discrete Mathematics 89 (1991) 149-160. For a Steiner triple system of order v to have a complete s-arc one must have s(s + 1)/2 3 v with equality only if s = 1 or 2 mod 4. To partition
Complete Arcs in Steiner Triple Systems
β Scribed by Charles J Colbourn; Jeffrey H Dinitz
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 394 KB
- Volume
- 80
- Category
- Article
- ISSN
- 0097-3165
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π SIMILAR VOLUMES
We establish that for all s, there exists a design with parameters (s', 3, 2) such that the points can be partitioned into s complete s-arcs. Furthermore we present a general technique which applies to the construction of designs (s', 4, 1) possessing a partition into s complete s-arcs. This gives a
## Abstract In this note, the 80 nonβisomorphic triple systems on 15 points are revisited from the viewpoint of the convex hull of the characteristic vectors of their blocks. The main observation is that the numbers, of facets of these 80 polyhedra are all different, thus producing a new proof of t
and v 15, a 3-chromatic Steiner triple system of order v all of whose 3-colorings are equitable. 1997 Academic Press ## 1. Introduction A Steiner triple system of order v (briefly STS(v)) is a pair (X, B), where X is a v-element set and B is a collection of 3-subsets of X (triples), such that eve