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math.CO2020
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…
math.CO2020
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…
math.CO2018
The linkedness of cubical polytopes
Hoa Thi 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…