Connectivity of cubical polytopes

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:169

Article

Bui, Hoa T.¹  Pineda-Villavicencio, Guillermo^1,2  Ugon, Julien^1,2 

[1] Federat Univ Australia, Ctr Informat & Appl Optimisat, Ballarat, Vic, Australia

[2] Deakin Univ, Sch Informat Technol, Geelong, Vic, Australia

关键词: Cube;    Hypercube;    Cubical polytope;    Connectivity;    Separator;   

DOI  :  10.1016/j.jcta.2019.105126

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free