We consider the problem of determining cp(G v KC), the smallest number of cliques required to partition the edge set of the graph G v K~, where G is a finite simple graph and K~, is the empty graph on m vertices. A lower bound on cp(G v K~,,,) is obtained which, when applied to the case G = K,, shar
Minimal pairwise balanced designs
โ Scribed by R.G. Stanton
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 276 KB
- Volume
- 77
- Category
- Article
- ISSN
- 0012-365X
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๐ SIMILAR VOLUMES
Let K = {k,, , k,} be a set of block sizes, and let (pr, , p,} be nonnegative numbers with Cy!',,p, = 1. We prove the following theorem: for any E >O, if a (u, K, 1) pairwise balanced design exists and v is sufficiently large, then a (u, K, 1) pairwise balanced design exists in which the fraction
An affine ฮฑ-resolvable PBD of index ฮป is a triple (V, B, R), where V is a set (of points), B is a collection of subsets of V (blocks), and R is a partition of B (resolution), satisfying the following conditions: (i) any two points occur together in ฮป blocks, (ii) any point occurs in ฮฑ blocks of each
It is shown that the block-intersection graph of a pairwise balance design with ),= l is edge-pancyclic given that its minimum block cardinality is at least 3.