Embedding a pair of graphs in a surface, and the width of 4-dimensional prismatoids

Details Embedding a pair of graphs in a surface, and the width of 4-dimensional prismatoids Embedding a pair of graphs in a surface, and the width of 4-dimensional prismatoids

2011-04-13

arxiv.org/abs/1104.2630v1

Discrete Comput. Geom. 47:3 (2012), 569-576

Mathematics

Combinatorics

This paper merges and supersedes the papers arXiv:1101.3050 (of the last two authors) and arXiv:1102.2645 (of the first author

Scientific paper

10.1007/s00454-011-9361-9

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.

Affiliated with

Also associated with

No associations

Rating

Embedding a pair of graphs in a surface, and the width of 4-dimensional prismatoids does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Embedding a pair of graphs in a surface, and the width of 4-dimensional prismatoids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Embedding a pair of graphs in a surface, and the width of 4-dimensional prismatoids will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-164765