Graphic vertices of the metric polytope
Discrete Mathematics - Special issue on graph theory and combinatorics
On Skeletons, Diameters and Volumes of Metric Polyhedra
Selected papers from the 8th Franco-Japanese and 4th Franco-Chinese Conference on Combinatorics and Computer Science
Geometry of Cuts and Metrics
The decomposition of the hypermetric cone into L-domains
European Journal of Combinatorics
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We show that the symmetry groups of the cut cone Cutn and the metric cone Metn both consist of the isometries induced by the permutations on $$\{1,\dots,n\}$$ , that is, $$Is(\mathrm{Cut}{n})=Is(\mathrm{Met}{n})\simeq Sym{n}$$ for n 驴 5. For n = 4 we have $$Is(\mathrm{Cut}{4})=Is(\mathrm{Met}{4})\simeq Sym{3}\times Sym{4}$$ . This result can be extended to cones containing the cuts as extreme rays and for which the triangle inequalities are facet-inducing. For instance, $$ Is ({\rm Hyp}_n) \simeq Sym(n)$$ for n 驴 5, where Hypn denotes the hypermetric cone.