A graph associahedron is a simple polytope whose face lattice encodes the
nested structure of the connected subgraphs of a given graph. In this paper, we
study certain graph properties of the 1-skeleta of graph associahedra, such as
their diameter and their Hamiltonicity. Our results extend known results for
the classical associahedra (path associahedra) and permutahedra (complete graph
associahedra). We also discuss partial extensions to the family of nestohedra.Comment: 26 pages, 20 figures. Version 2: final version with minor correction