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

@article{Averkov2013OnMS,
  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.},
  year={2013},
  volume={27},
  pages={1610-1624}
}
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

From This Paper

Topics from this paper.

Citations

Publications citing this paper.
Showing 1-10 of 10 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 29 references

Convexity in crystallographical lattices

  • J.-P. Doignon
  • J. Geometry, 3
  • 1973
Highly Influential
11 Excerpts

A proof of Lovász’s theorem on maximal lattice-free sets

  • G. Averkov
  • Beitr. Algebra Geom., 54
  • 2013
Highly Influential
7 Excerpts

Transversal numbers over subsets of linear spaces

  • G. Averkov, R. Weismantel
  • Adv. Geom., 12
  • 2012
Highly Influential
4 Excerpts

Inequalities for the lattice width of lattice-free convex sets in the plane, Beitr

  • G. Averkov, Ch. Wagner
  • Algebra Geom.,
  • 2012

Ch

  • G. Averkov
  • Wagner, and R. Weismantel, Maximal lattice-free…
  • 2011
1 Excerpt

A cutting plane theory for mixed integer optimization

  • R. Weismantel
  • Proceedings of the International Congress of…
  • 2010
1 Excerpt

Similar Papers

Loading similar papers…