Enclaveless Sets and MK-Systems.

A hypergraph H = ( X , E ) is called a Menger System if the maximum cardinality of a family of pairwise disjoint edges (v 1(H)) is equal to the minimum cardinality of a subset of vertices which meets every edge (τ 0(H)). A set S ⊆ X is defined to be enclaveless if each vertex in S is adjacent to at least one vertex in X - S. A parameter π 0 related to the formation of maximal enclaveless sets is defined, and it is shown that if H has no singleton edges then v 1(H) ≤ π 0(H). MK-Systems are defined to be those hypergraphs H without singleton edges for which v 1(H) = π 0(H); simple graphs which are Menger Systems are shown also to be MK-Systems.