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Connectivity of cubical polytopes
journal contribution
posted on 2020-01-01, 00:00 authored by Hoa T Bui, Guillermo Pineda VillavicencioGuillermo Pineda Villavicencio, Julien UgonJulien UgonA 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 δ is {δ,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.
History
Journal
Journal of Combinatorial Theory, Series AVolume
169Article number
105126Pagination
1 - 21Publisher
ElsevierLocation
Amsterdam, The NetherlandsPublisher DOI
ISSN
0097-3165eISSN
1096-0899Language
engPublication classification
C1 Refereed article in a scholarly journalUsage metrics
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