Dukes, Peter J.Ling, Alan C. H.Malloch, Amanda2021-02-092021-02-0920162016Dukes, P. J., Ling, A. C. H., & Malloch, A. (2016). Thickly-resolvable block designs . The Australasian Journal of Combinatorics, 64(2). https://ajc.maths.uq.edu.au/pdf/64/ajc_v64_p379.pdfhttps://ajc.maths.uq.edu.au/pdf/64/ajc_v64_p379.pdfhttp://hdl.handle.net/1828/12670We show that the necessary divisibility conditions for the existence ofaσ-resolvable BIBD(v,k,λ) are sufficient for largev. The key idea isto form an auxiliary graph based on an [r,k]-configuration withr=σ,and then edge-decompose the completeλ-fold graphK(λ)vinto this graph.As a consequence, we initiate a similar existence theory for incompletedesigns with indexλenArticleDepartment of Mathematics and Statistics