It is shown that if F1, F2, . . . , Ft are bipartite 2-regular graphs of order n and Î±1, Î±2, . . . , Î±t are non-negative integers such that Î±1+Î±2+Â· Â· Â·+Î±t = nâˆ’2 2 , Î±1 â‰¥ 3 is odd, and Î±i is even forâ€¦ (More)

A resolvable modified group divisible design (RMGDD) is an MGDD whose blocks can be partitioned into parallel classes. In this article, we investigate the existence of RMGDDs with block size threeâ€¦ (More)

We consider Class-Uniformly Resolvable Group Divisible Designs (CURGDD), which are resolvable group divisible designs in which each of the resolution classes has the same number of blocks of eachâ€¦ (More)

A central question in design theory dating from Kirkman in 1850 has been the existence of resolvable block designs. In this paper we will concentrate on the case when the block size k = 4. Theâ€¦ (More)

The 2-parallel chromatic index X" (8) is the minimum number of colours required to colour the blocks of a Steiner triple system 8 so that any two parallel blocks receive different colours. The valueâ€¦ (More)

We consider Class-Uniformly Resolvable frames (CURFs), which are group divisible designs with partial resolution classes subject to the class-uniform condition. We derive the necessary conditions,â€¦ (More)

If G = (V â€², E) is a graph and H = (V, H) is a graph whose edges can be decomposed into isomorphic copies of G, then we define a k-block colouring of a Gâˆ’decomposition of H to be an assignment of kâ€¦ (More)

In this paper we examine the resolvability of infinite designs. We show that in stark contrast to the finite case, resolvability for infinite designs is fairly commonplace. We prove that every t-(v,â€¦ (More)