More-Than-Nearly-Perfect Packings and Partial Designs


(n) of the n vertices. Here we show, in particular, that regular uniform hypergraphs for which the ratio of degree to maximum codegree is , for some ɛ>0, have packings which cover all but vertices, where α=α(ɛ)>0.

The proof is based on the analysis of a generalized version of Rödl's nibble technique.

We apply the result to the problem of finding partial Steiner systems with almost enough blocks to be Steiner systems, where we prove that, for fixed positive integers t<k, there exist partial S(t,k,n)'s with at most uncovered t-sets, improving the earlier result.

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Received: September 23, 1994/Revised: November 14, 1996

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Grable, D. More-Than-Nearly-Perfect Packings and Partial Designs. Combinatorica 19, 221–239 (1999).

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  • AMS Subject Classification (1991) Classes:  05C70, 05B05