Chromatic numbers for facet colouring of some generalised associahedra (Q6611074)

In this paper, the authors study combinatorial properties of generalised associahedra. A proper facet coloring of a polytope \(\mathcal P\) is an assignment of colors to the facets of \(\mathcal P\) such that two facets sharing a vertex have distinct colors. The minimum number of colors necessary for such a coloring is determined exactly for permutohedra, associahedra and simple permutoassociahedra, while bounds are proved for cyclohedra, and so-called stellohedra. In some cases the authors also obtain asymptotic values of the minimum number of colors needed for such a coloring.