On Maximal S-Free Sets and the Helly Number for the Family of S-Convex Sets

  title={On Maximal S-Free Sets and the Helly Number for the Family of S-Convex Sets},
  author={Gennadiy Averkov},
  journal={SIAM J. Discrete Math.},
We study two combinatorial parameters, which we denote by f(S) and h(S), associated with an arbitrary set S ⊆ Rd, where d ∈ N. In the nondegenerate situation, f(S) is the largest possible number of facets of a d-dimensional polyhedron L such that the interior of L is disjoint with S and L is inclusion-maximal with respect to this property. The parameter h(S) is the Helly number of the family of all sets that can be given as the intersection of S with a convex subset of Rd. We obtain the… CONTINUE READING

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