o
(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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: September 23, 1994/Revised: November 14, 1996
Rights and permissions
About this article
Cite this article
Grable, D. More-Than-Nearly-Perfect Packings and Partial Designs. Combinatorica 19, 221–239 (1999). https://doi.org/10.1007/s004930050053
Issue Date:
DOI: https://doi.org/10.1007/s004930050053