Facets of the \(p\)-cycle polytope (Q5946821)

This paper studies the convex hull of all incidence vectors of simple directed cycles consisting of \(p\) arcs in the complete directed graph \(K_n\). After determining the dimension as a function of \(n\) and \(p\), various other polyhedral results are given. They include a description of the bases of the equality set, two lifting results, and various aspects of valid inequalities and facets. Finally, the relationship to the \(p\)-circuit polytope is investigated, which is the corresponding structure on undirected graphs.