Chromatic numbers for facet colouring of some generalised associahedra

The chromatic number related to a colouring of facets of certain classes of generalised associahedra is studied. The exact values are obtained for permutohedra, associahedra and simple permutoassociahedra, while lower and upper bounds are established for cyclohedra and stellohedra. The asymptotic values of the chromatic numbers for associahedra, cyclohedra and simple permutoassociahedra are given.