Minimal Enclosing of an MPT （v,λ） in a TS （u,λ＋1）

Let MPT (v,λ) denote a maximum packing of triples of order v with index λ and TS (u,λ) denote a triple system of order u with index λ. In this paper, for v≥6, we determine necessary and sufficient condition for enclosing an MPT (v,λ) in a TS (v m,λ 1) with index λ increased by 1 and minimal increase in extra points.     

Minimal Enclosing of an MPT (v,λ) in a TS (v+1,μ)

IntroductionA maximum packing of triples( or simply amaximum packing) of order v with indexλ,denot-ed by MPT( v,λ) ,is a pair( V,B) where V is a v-set and B is a collection of 3- subsets ( called blocksor triples) of V such that1 each2 - subset of V iscontained in atmostλ triples,2 if C is any collec-tion of 3- subsets satisfying 1 then | B|≥ | C| .Let ( V,B) be an MPT ( v,λ) ,the leave of ( V,B) ,denoted by L ( v,λ) ,is a multigraph( V,E)when an edge {x,y}∈ E with multiplicity…