Abstract
LetC andA be (0, 1)-valued matrices with no zero columns. Fulkerson has shown that the extreme points of {x: Cx ≤ 1,x ≥ 0} are given by the rows ofA and their projections and the extreme points of {x: Ax ≤ 1,x ≥ 0} are given by the rows ofC and their projections if and only if the maximal rows ofC andA are the incidence vectors of maximal cliques and anticliques, respectively, of a perfect graph. This theorem is discussed and a new proof is given for the “only if” implication.
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Research partially supported by grant ENG 76-09936 from the National Science Foundation to Cornell University and by Sonderforschungsbereich 21 (DFG), Institut für Operations Research, Universität Bonn.
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Monma, C.L., Trotter, L.E. On perfect graphs and polyhedra with (0, 1)-valued extreme points. Mathematical Programming 17, 239–242 (1979). https://doi.org/10.1007/BF01588246
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DOI: https://doi.org/10.1007/BF01588246