On Skeletons , Diameters and Volumesof Metric PolyhedraAntoine DEZA

On Skeletons, Diameters and Volumes of Metric Polyhedra

Abst rac t . We survey and present new geometric and combinatorial propertiez of some polyhedra with application in combinatorial optimization, for example, the max-cut and multicommodity flow problems. Namely we consider the volume, symmetry group, facets, vertices, face lattice, diameter, adjacency and incidence relm :ons and connectivity of the metric polytope and its relatives. In partic~da...

Skeletons of Some Relatives of the N-cube Skeletons of Some Relatives of the N-cube

We study the skeleton of several polytopes related to the n-cube, the halved n-cube, and the folded n-cube. In particular, the Gale polytope of the n-cube, its dual and the duals of the halved n-cube and the complete bipartite sub-graphs polytope.

Note on Half-cube Embeddings

We establish some results on embeddings in half-cube graphs. They are motivated by M. Deza, M. Dutour Sikirić, and S. Shpectorov’s conjecture [1] concerning isometric embeddings of the skeletons of polytope Wythoffians in half-cube graphs.

On simplicial and cubical complexes with short links

We consider closed simplicial and cubical n-complexes in terms of link of their (n−2)faces. Especially, we consider the case, when this link has size 3 or 4, i.e., every (n − 2)face is contained in 3 or 4 n-faces. Such simplicial complexes with short (i.e. of length 3 or 4) links are completely classified by their characteristic partition. We consider also embedding into hypercubes of the skele...

GeometryofCutsand Metrics