Integral Boundary Points of Convex Polyhedra

Alan J. Hoffman () and Joseph B. Kruskal ()
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Alan J. Hoffman: IBM Research
Joseph B. Kruskal: Bell Laboratories

Chapter Chapter 3 in 50 Years of Integer Programming 1958-2008, 2010, pp 49-76 from Springer

Abstract: Abstract Here is the story of how this paper was written. (a) Independently, Alan and Joe discovered this easy theorem: if the “right hand side” consists of integers, and if the matrix is “totally unimodular”, then the vertices of the polyhedron defined by the linear inequalities will all be integral. This is easy to prove and useful. As far as we know, this is the only part of our theorem that anyone has ever used.

Keywords: Linear Inequality; Convex Polyhedron; Birthday Party; Combinatorial Theorem; Unimodular Matrice (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-540-68279-0_3

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