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There are two topics in this pdf (Maximum Packings + Minimum coverings). Choose one of them and make summary and solve three questions. I need three pages for this assignment.
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Maximum Packings Summary
Maximum packings constructions are divided into four parts which mainly are dependent on
leave. the simplest form is when L=∅ , then for such a situation:
Maximum packing is equal to Steiner triple system.
on the other hand, 1-factor construction:
v=0, and if Steiner triple system is |𝑆|=v+ 1. Letting L= {{a,b} |{ꝏ, a, b} εT
Then the maximum packing in the order of v with a leave of 1-factor L is given by:
(S/ {ꝏ}. T/T (ꝏ), L). Hence 6n+1 or 6n+3 being Steiner Triple System. Therefore, packing for
a 1-factor leave is given in the order 6n +(0 or 2)
The four-cycle construction, assume that v≡5 which is in (mod 6) and assuming that (P,B) is a
block known as PBD that has a a block size of 5 and the other remaining blocks are with sies of
3. On the other hand, it is assumed that T is triple set in B. Further replace the blocks with
{a,b,c,d,e} for the blocs with size 5 and let the maximum packing be ({a, b...