Colorful polytopes and graphs
Por:
Araujo-Pardo G., Hubard I., Oliveros D., Schulte E.
Publicada:
1 jun 2013
Categoría:
Mathematics (miscellaneous)
Resumen:
The paper investigates connections between abstract polytopes and
properly edge colored graphs. Given any finite n-edge-colored n-regular
graph G, we associate to G a simple abstract polytope P (G) of rank n,
the colorful polytope of G, with 1-skeleton isomorphic to G. We
investigate the interplay between the geometric, combinatorial, or
algebraic properties of the polytope P (G) and the combinatorial or
algebraic structure of the underlying graph G, focussing in particular
on aspects of symmetry. Several such families of colorful polytopes are
studied including examples derived from a Cayley graph, in particular
the graphicahedra, as well as the flagadjacency polytopes and related
monodromy polytopes associated with a given abstract polytope. The duals
of certain families of colorful polytopes have been important in the
topological study of colored triangulations and crystallization of
manifolds.
Filiaciones:
Araujo-Pardo G.:
Univ Nacl Autonoma Mexico, Inst Matemat, Area Invest Cient, Mexico City 04510, DF, Mexico
Hubard I.:
Univ Nacl Autonoma Mexico, Inst Matemat, Area Invest Cient, Mexico City 04510, DF, Mexico
Oliveros D.:
Univ Nacl Autonoma Mexico, Inst Matemat, Area Invest Cient, Mexico City 04510, DF, Mexico
Schulte E.:
Department of Mathematics, Northeastern University, Boston, MA, 02115, United States
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