Graph properties of graph associahedra

Thibault Manneville (1) , Vincent Pilaud (1)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

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.

Mots clés: Graph associahedron; nestohedron; graph diameter; Hamiltonian cycle

Domaines: Combinatoire [math.CO]

Thibault Manneville, Vincent Pilaud. Graph properties of graph associahedra. Seminaire Lotharingien de Combinatoire, 2015, 73, pp.B73d. ⟨hal-01276806⟩