Abstract
In a series of 2 papers, Kang, Du and Tian solved the existence problem for G-decomposition of λ K n when G is any simple graph with 6 vertices and 7 edges, except when G is the graph T=K 4∪K 2. Notice that a T-decomposition can be considered to be a Pairwise Balanced Design in which each block of size 4 has been matched to a block of size 2. In this paper we remove this exception for all λ≥2. The case when λ=1 is also addressed.
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References
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This paper is written in honor of Frank Hwang on the occasion of his 65th birthday.
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Rodger, C.A., Westbrook, S.K. Decompositions of λ K v . J Comb Optim 14, 259–265 (2007). https://doi.org/10.1007/s10878-007-9056-6
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DOI: https://doi.org/10.1007/s10878-007-9056-6