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Coxeter complexes and graph-associahedra. (English) Zbl 1099.52001
The authors suggest a construction of a simple convex polytope, called graph-associahedra, which is associated with a given graph Γ and whose face partial order coincides with the partial order of sets of connected subgraphs of Γ. This construction includes as particular cases the Stasheff associahedron and the Bott-Taubes cyclohedron. In case of simplicial Coxeter groups and respective Coxeter complexes the graph-associahedron represents its fundamental domain. Furthermore, the minimal blow-ups of such Coxeter complexes have tiling by graph-associahedra, which can be viewed as a generalization of the Deligne-Knudsen-Mumford compactification of the real moduli space of rational curves with marked points.

MSC:
52B05Combinatorial properties of convex sets
05B45Tessellation and tiling problems
05C70Factorization, etc.