Base polyhedra and the linking property

Tamás Király ()
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Tamás Király: ELTE Eötvös Loránd University

Journal of Combinatorial Optimization, 2018, vol. 36, issue 3, No 1, 677 pages

Abstract: Abstract An integer polyhedron $$P \subseteq {\mathbb {R}}^n$$ P ⊆ R n has the linking property if for any $$f \in {\mathbb {Z}}^n$$ f ∈ Z n and $$g \in {\mathbb {Z}}^n$$ g ∈ Z n with $$f \le g$$ f ≤ g , P has an integer point between f and g if and only if it has both an integer point above f and an integer point below g. We prove that an integer polyhedron in the hyperplane $$\sum _{j=1}^n x_j=\beta $$ ∑ j = 1 n x j = β is a base polyhedron if and only if it has the linking property. The result implies that an integer polyhedron has the strong linking property, as defined in Frank and Király (in: Cook, Lovász, Vygen (eds) Research trends in combinatorial optimization, Springer, Berlin, pp 87–126, 2009), if and only if it is a generalized polymatroid.

Keywords: Integer polyhedron; Linking property; Base polyhedron; Polymatroid (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-017-0133-1

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