A Note on Range-Restricted Circuit Covers

 Let Cone(G), Int.Cone(G) and Lat(G) be the cone, the integer cone and the lattice of the incidence vectors of the circuits of graph G. A good range is a set ?⊆ℕ such that Cone (G)∩Lat (G)∩?^E⊆Int.Cone(G) for every graph G(V,E). We give a counterexample to a conjecture of Goddyn 1] stating that ℕ\{1} is a good range. Received: November 26, 1997