Israel Journal of Mathematics

, Volume 192, Issue 1, pp 121–141 | Cite as

Polytopality and Cartesian products of graphs

Article

Abstract

We study the question of polytopality of graphs: when is a given graph the graph of a polytope? We first review the known necessary conditions for a graph to be polytopal, and we present three families of graphs which satisfy all these conditions, but which nonetheless are not graphs of polytopes.

Our main contribution concerns the polytopality of Cartesian products of non-polytopal graphs. On the one hand, we show that products of simple polytopes are the only simple polytopes whose graph is a product. On the other hand, we provide a general method to construct (non-simple) polytopal products whose factors are not polytopal.

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Copyright information

© Hebrew University Magnes Press 2012

Authors and Affiliations

  • Julian Pfeifle
    • 1
  • Vincent Pilaud
    • 2
  • Francisco Santos
    • 3
  1. 1.Departament de Matemàtica Aplicada IIUniversitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Laboratoire d’Informatique de l’École PolytechniqueÉcole PolytechniquePalaiseau CedexFrance
  3. 3.Departamento de Matemáticas Estadística y ComputaciónUniversidad de CantabriaSantanderSpain

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