Some new resolvable GDDs with k=4 and doubly resolvable GDDs with k=3

Doubly resolvable designs with small parameters

Doubly resolvable 2-(v,k,λ) designs (DRDs) with small parameters and their resolutions which have orthogonal resolutions (RORs) are constructed and classified up to isomorphism. Exact values or lower bounds on the number of the nonisomorphic sets of m mutually orthogonal resolutions (m-MORs) are presented. The implemented algorithms and the parameter range of this method are discussed, and the ...

Some new near resolvable BIBDs with k=7 and resolvable BIBDs with k=5

Existence of (K4-e)-GDDs of type 2n

Suppose Kv is the complete undirected graph with v vertices. Let K4 − e be the graph obtained from K4 by removing one edge. A (K4 − e) group divisible design (briefly (K4 − e)-GDD) of type h is a triple (X,G,B), where G is a partition of X into groups each of size h, B is an edge-disjoint decomposition of the edge set of Kh,h,...,h, the multipartite complete undirected graph with G as the parti...

Doubly near resolvable m-cycle systems

An m-cycle system C of λKn is said to be near resolvable if the mcycles in C can be partitioned into near parallel classes R1, R2, . . . , Rλn/2, each one of which is a 2-factor of λKn − v for some vertex v in λKn. If an NR(n,m, λ)-CS has a pair of orthogonal resolutions, it is said to be doubly resolvable and is denoted by DNR(n,m, λ)-CS. For m = 2, 3, DNR(n,m, 2)-CSs are known as Room frames ...

Orthogonal 3-GDDs with four groups

Consider a pair of group divisible designs (GDD) with block size 3, index λ = 1, and on the same points and groups. They are said to be orthogonal (OGDD) if (i) whenever two blocks, one from each design, intersect in two points, the third points are in different groups; and (ii) two disjoint pairs of points defining intersecting triples in one GDD fail to do so in the other. A question posed by...