- Title
- Connectivity of cubical polytopes
- Creator
- Bui, Hoa; Pineda-Villavicencio, Guillermo; Ugon, Julien
- Date
- 2019
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/171194
- Identifier
- vital:14273
- Identifier
-
https://doi.org/10.1016/j.jcta.2019.105126
- Identifier
- ISBN:0097-3165
- Abstract
- A cubical polytope is a polytope with all its facets being combinatorially equivalent to cubes. We deal with the connectivity of the graphs of cubical polytopes. We first establish that, for any d >= 3, the graph of a cubical d-polytope with minimum degree 5 is min{delta, 2d - 2}-connected. Second, we show, for any d >= 4, that every minimum separator of cardinality at most 2d - 3 in such a graph consists of all the neighbours of some vertex and that removing the vertices of the separator from the graph leaves exactly two components, with one of them being the vertex itself. (C) 2019 Elsevier Inc. All rights reserved.
- Relation
- Journal of Combinatorial Theory Series A Vol. 169, no. (Jan 2019), p. 21
- Rights
- © 2019 Elsevier Inc. All rights reserved.
- Rights
- This metadata is freely available under a CCO license
- Rights
- Open Access
- Subject
- 0101 Pure Mathematics; Cube; Hypercube; Cubical polytope; Connectivity; Separator
- Full Text
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