The Stein-LovÃ¡sz Theorem can be used to get existence results for some combinatorial problems using constructive methods rather than probabilistic methods. In this paper, we discuss applications ofâ€¦ (More)

Let v be a positive integer, and K and M be two sets of positive integers. A group divisible design GD(K;M ; v) is an ordered triple (X,G,B) where X is a set with cardinality v, G is a set of subsetsâ€¦ (More)

In this paper we further discuss the embedding problem for nearly Kirkman triple systems and get the result that: (1) For u â‰¡ v â‰¡ 0 (mod 6), vÂ¿ 78, and uÂ¿ 3:5v, there exists an NKTS(u) containing aâ€¦ (More)

For given positive integers u and v with u â‰¡ v â‰¡ 0 (mod 6), let IRC(u; v) denote an incomplete resolvable minimum covering of pairs by triples of order u having a hole of size v. It is proved in thisâ€¦ (More)

For a given positive integer v with v â‰¡ 4(mod 6) and v > 4, let CKPD(v) denote a canonical Kirkman packing design of order v. It is proved in this paper that any CKPD(v) can be embedded in a CKPD(u)â€¦ (More)

It is proved in this paper that for hâˆˆ{6; 12}, there exists an incomplete nearly Kirkman triple system (NKTS) of order v having a hole of size h if and only if v â‰¡ 0 (mod 6) and vÂ¿ 3h, thus providingâ€¦ (More)