The Combinatorial Structure of Small
Cut and Metric Polytop es
Antoine DEZA
Michel DEZA
Lab oratoire d Informatique URA du CNRS
D epartement de Math ematiques et d Informatique
Ecole Normale Sup erieure
LIENS
January
The Combinatorial Structure of Small Cut and
Metric Polytop es
Antoine DEZA Michel DEZA
January
Abstract We study the combinatorial structure of the cut and metric p olytop es on n
no des for n Those two p olytop es have a complicated geometrical structure but using
their large symmetry group we can completely describ e their face lattices We present
for any n some orbits of faces and give new result on the tightness of the wrapping of
the cut p olytop e by the metric p olytop e disproving a conjecture of on their lattices
Key words metric p olytop e complete bipartite subgraphs p olytop e face lattice