14 citations · 46 across the 26 of their papers we have counts for
6 papers · 1 filter
Linkedness of Cartesian products of complete graphs
Leif K. Jorgensen, Guillermo Pineda-Villavicencio, Julien Ugon
This paper is concerned with the linkedness of Cartesian products of complete graphs. A graph with at least vertices is {\it -linked} if, for every set of distinct ver…
Reconstructibility of matroid polytopes
Guillermo Pineda-Villavicencio, Benjamin Schröter
We specify what is meant for a polytope to be reconstructible from its graph or dual graph. And we introduce the problem of class reconstructibility, i.e., the face lattice of the…
The linkedness of cubical polytopes: The cube
Hoa T. Bui, Guillermo Pineda-Villavicencio, Julien Ugon
The paper is concerned with the linkedness of the graphs of cubical polytopes. A graph with at least vertices is \textit{-linked} if, for every set of disjoint pairs of…
The linkedness of cubical polytopes: beyond the cube
Hoa T. Bui, Guillermo Pineda-Villavicencio, Julien Ugon
A cubical polytope is a polytope with all its facets being combinatorially equivalent to cubes. The paper is concerned with the linkedness of the graphs of cubical polytopes. A gra…
A new proof of Balinski's theorem on the connectivity of polytopes
Guillermo Pineda-Villavicencio
Balinski (1961) proved that the graph of a -dimensional convex polytope is -connected. We provide a new proof of this result. Our proof provides details on the nature of a se…
Minimum number of edges of polytopes with 2d + 2 vertices
Guillermo Pineda-Villavicencio, Julien Ugon, David Yost
We define an analogue of the cube and an analogue of the 5-wedge in higher dimensions, each with vertices and edges. We show that these two are the only minimiser…