On a geometric property of perfect graphs

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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Zaremba, L.S., Perz, S. On a geometric property of perfect graphs. Combinatorica 2, 395–397 (1982). https://doi.org/10.1007/BF02579436

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AMS subject classification 1980

  • 05 C 99
  • 52 A 25