Abstract
LetG be a graph,VP(G) its vertex packing polytope and letA(G) be obtained by reflectingVP(G) in all Cartersian coordinates. Denoting byA*(G) the set obtained similarly from the fractional vertex packing polytope, we prove that the segment connecting any two non-antipodal vertices ofA(G) is contained in the surface ofA(G) and thatG is perfect if and only ifA*(G) has a similar property.
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