On the cycle polytope of a binary matroid

Abstract

The convex hull of the incidence vectors of the cycles of a binary matroid is studied. We prove that a description of the facets of this polytope can be obtained from a description of the facets that contain any given vertex. The facet-inducing inequalities are given for matroids with no F 7 ∗ , R 10, or M(K 5) ∗ minor. We also characterize adjacency on this polytope.