scholarly journals On the cone of $f$-vectors of cubical polytopes

2019 ◽  
Vol 147 (5) ◽  
pp. 1851-1866 ◽  
Author(s):  
Ron M. Adin ◽  
Daniel Kalmanovich ◽  
Eran Nevo
Keyword(s):  
Cubical Polytopes

scholarly journals Neighborly cubical polytopes and spheres

2007 ◽  
Vol 159 (1) ◽  
pp. 221-242 ◽  
Author(s):  
Michael Joswig ◽  
Thilo Rörig
Keyword(s):  
Cubical Polytopes

scholarly journals The Linkedness of Cubical Polytopes: The Cube

10.37236/9848 ◽  
2021 ◽  
Vol 28 (3) ◽  
Author(s):  
Hoa T. Bui ◽  
Guillermo Pineda-Villavicencio ◽  
Julien Ugon
Keyword(s):  
Disjoint Paths ◽  
Cubical Polytopes ◽  
Dimensional Cube ◽  
Vertex Disjoint

The paper is concerned with the linkedness of the graphs of cubical polytopes. A graph with at least $2k$ vertices is $k$-linked if, for every set of $k$ disjoint pairs of vertices, there are $k$ vertex-disjoint paths joining the vertices in the pairs. We say that a polytope is $k$-linked if its graph is $k$-linked. We establish that the $d$-dimensional cube is $\lfloor (d+1)/2 \rfloor$-linked, for every $d\ne 3$; this is the maximum possible linkedness of a $d$-polytope. This result implies that, for every $d\geqslant 1$, a cubical $d$-polytope is  $\lfloor d/2\rfloor$-linked, which answers a question of Wotzlaw (Incidence graphs and unneighborly polytopes, Ph.D. thesis, 2009).  Finally, we introduce the notion of strong linkedness, which is slightly stronger than that of linkedness. A graph $G$ is strongly $k$-linked if it has at least $2k+1$ vertices and, for  every vertex $v$ of $G$, the subgraph $G-v$ is $k$-linked. We show that cubical 4-polytopes are strongly $2$-linked and that, for each $d\geqslant 1$,  $d$-dimensional cubes  are strongly $\lfloor d/2\rfloor$-linked. 

scholarly journals Connectivity of cubical polytopes

2020 ◽  
Vol 169 ◽  
pp. 105126
Author(s):  
Hoa T. Bui ◽  
Guillermo Pineda-Villavicencio ◽  
Julien Ugon
Keyword(s):  
Cubical Polytopes

scholarly journals Gaps in the numbers of vertices of cubical polytopes, I

1994 ◽  
Vol 11 (3) ◽  
pp. 351-356 ◽  
Author(s):  
G. Blind ◽  
R. Blind
Keyword(s):  
Cubical Polytopes

scholarly journals The almost simple cubical polytopes

1998 ◽  
Vol 184 (1-3) ◽  
pp. 25-48 ◽  
Author(s):  
G. Blind ◽  
R. Blind
Keyword(s):  
Cubical Polytopes

scholarly journals Neighborly Cubical Polytopes

2000 ◽  
Vol 24 (2) ◽  
pp. 325-344 ◽  
Author(s):  
M. Joswig ◽  
G. M. Ziegler
Keyword(s):  
Cubical Polytopes

scholarly journals The lower and upper bound problems for cubical polytopes

1993 ◽  
Vol 9 (2) ◽  
pp. 159-163 ◽  
Author(s):  
William Jockusch
Keyword(s):  
Upper Bound ◽  
Cubical Polytopes
Sign in / Sign up

Export Citation Format

Share Document