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Decompositions of complete graphs into factors with diameter two. (English) Zbl 0213.51003
Let \(f(k)\) be the smallest integer \(n\) so that the complete graph \(\langle n \rangle\) can be decomposed into \(k\) edge disjoint subgraphs of diameter \(2\). The authors prove: (1) \(f(k)<\left({49 \over 10} \right)^2k^2 \log k\). Recently N. Sauer considerably improved (1) by showing \(f(k)<7k\) [cf. the paper reviewed below, J. Comb. Theory 9, 423-426 (1970; Zbl 0213.51004)].

05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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