Abstract
Let E be a finite set and \({\mathcal{H}}\) a family of subsets of E such that the symmetric difference of any two members of this family is at least 2. Let \({\mathcal{F}}\) be the complement of \({\mathcal{H}}\) in \({\mathcal{P}(E)}\), the set of the subsets of E. In this paper we characterize the convex hull of the characteristic vectors of the elements of \({\mathcal{F}}\). We consider also the polar of these polyhedra and study their links with some well known polyhedra.
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References
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Note from the Author
During the final meeting on graph theory organized by Claude Berge in Marseille, held in 2000, I discussed the initial ideas in this paper with Vašek Chvátal. I have presented these results in Maurras (2001). Independently, Lee (2003) has worked on the same subject and developed it in other directions.
Note from the Editors
This paper was originally submitted directly to a guest editor appointed for a planned special issue dedicated to the memory of Claude Berge. Unfortunately the issue never materialized and had to be canceled. It was only recently discovered that this paper was never processed.
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Maurras, J.F. A family of easy polyhedra. 4OR-Q J Oper Res 7, 139–144 (2009). https://doi.org/10.1007/s10288-008-0079-3
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DOI: https://doi.org/10.1007/s10288-008-0079-3