@article{GILES1979191,
    Abstract = {A linear system Ax ⩽ b (A, b rational) is said to be totally dual integral (TDI) if for any integer objective function c such that max {cx: Ax ⩽ b} exists, there is an integer optimum dual solution. We show that if P is a polytope all of whose vertices are integer valued, then it is the solution set of a TDI system Ax ⩽ b where b is integer valued. This was shown by Edmonds and Giles [4] to be a sufficient condition for a polytope to have integer vertices.},
    Author = {Giles, F.R. and Pulleyblank, W.R.},
    File = {Total dual integrality and integer polyhedra - a - a - a - t.pdf},
    ISSN = {0024-3795},
    Journal = {Linear Algebra and its Applications},
    Pages = {191 - 196},
    Title = {Total dual integrality and integer polyhedra},
    URL = {http://www.sciencedirect.com/science/article/pii/0024379579900181},
    Volume = {25},
    Year = {1979},
    bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/0024379579900181},
    bdsk-url-2 = {https://doi.org/10.1016/0024-3795(79)90018-1},
    date-added = {2020-02-25 08:19:12 +0100},
    date-modified = {2020-02-25 08:19:12 +0100},
    doi = {10.1016/0024-3795(79)90018-1}
}

@article{GILES1979191, Abstract = {A linear system Ax ⩽ b (A, b rational) is said to be totally dual integral (TDI) if for any integer objective function c such that max {cx: Ax ⩽ b} exists, there is an integer optimum dual solution. We show that if P is a polytope all of whose vertices are integer valued, then it is the solution set of a TDI system Ax ⩽ b where b is integer valued. This was shown by Edmonds and Giles [4] to be a sufficient condition for a polytope to have integer vertices.}, Author = {Giles, F.R. and Pulleyblank, W.R.}, File = {Total dual integrality and integer polyhedra - a - a - a - t.pdf}, ISSN = {0024-3795}, Journal = {Linear Algebra and its Applications}, Pages = {191 - 196}, Title = {Total dual integrality and integer polyhedra}, URL = {http://www.sciencedirect.com/science/article/pii/0024379579900181}, Volume = {25}, Year = {1979}, bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/0024379579900181}, bdsk-url-2 = {https://doi.org/10.1016/0024-3795(79)90018-1}, date-added = {2020-02-25 08:19:12 +0100}, date-modified = {2020-02-25 08:19:12 +0100}, doi = {10.1016/0024-3795(79)90018-1} }