The authors suggest a construction of a simple convex polytope, called graph-associahedra, which is associated with a given graph
and whose face partial order coincides with the partial order of sets of connected subgraphs of
. 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.