Embedding a Pair of Graphs in a Surface, and the Width of 4-dimensional Prismatoids

Santos, Francisco; Stephen, Tamon et Thomas, Hugh (2012). « Embedding a Pair of Graphs in a Surface, and the Width of 4-dimensional Prismatoids ». Discrete & Computational Geometry, 47(3), pp. 569-576.

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Résumé

A prismatoid is a polytope with all its vertices contained in two parallel facets, called its bases. Its width is the number of steps needed to go from one base to the other in the dual graph. The first author recently showed that the existence of counter-examples to the Hirsch conjecture is equivalent to that of d-prismatoids of width larger than d, and constructed such prismatoids in dimension five. Here we show that the same is impossible in dimension four. This is proved by looking at the pair of graph embeddings on a 2-sphere that arise from the normal fans of the two bases of Q.

Type:	Article de revue scientifique
Mots-clés ou Sujets:	Polytope, Polytope diameter, Hirsch conjecture, Graph embedding Prismatoid
Unité d'appartenance:	Faculté des sciences > Département de mathématiques
Déposé par:	Hugh R. Thomas
Date de dépôt:	18 mai 2016 19:51
Dernière modification:	30 mai 2016 20:18
Adresse URL :	http://archipel.uqam.ca/id/eprint/8498

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