We survey known results on the existence and enumeration of many kinds of 1-factorizations of the complete graph. We also mention briefly some related questions and topics, as well as applications.

One-factorizations of the complete graph—A survey

The packing and covering problem for the metric space J3J consisting of g-ary words of length n and provided with the deletion and insertion metric is considered. For any n = 1,2,... partitions of Β ζ and of the permutation set Sn (Sn C B%) into perfect codes capable of correcting single deletions are given. In connection with the problem of finding perfect codes capable of correcting s deletions a problem of constructing .ordered Steiner systems is stated, and a solution of this problem for some values of parameters is presented. For n = 3 and any q as well as for n = 4 and any even q, perfect in B* codes capable of correcting single deletions are constructed. An asymptotic behaviour of the maximum cardinality of a code in B" capable of correcting single deletions in case q/n —> oo is found .

On perfect codes in deletion and insertion metric

Cyclic Block Designs With Block Size 3

Two earlier versions of our bibliography on Steiner systems [D44], [D44.1] listed 400 and 675 titles, respectively. The number of papers concerning Steiner systems continues to grow, and the present listing contains already some 730 titles; all additions are recent papers. As for inclusion into our bibliography of papers dealing with finite projective, affine or inversive spaces, we follow the same policy as in [D44] and [D44.1] Information about reviews in referative journals is attached to the titles in the bibliography; MR stands for Mathematical Reviews while Z stands for Zentral-blatt fur Mathematik und ihre Grenzgebiete.

An Updated Bibliography and Survey of Steiner Systems

An isomorphic factorization of a graph is a decomposition into isomorphic edge-disjoint subgraphs. A number of new and old open problems on isomorphic factorizations are presented along with some existing related results.

Stephen H.Y Hung

Papers

Directed triple systems

On Howell designs