Properties and Classification of the Wheels of the OLS Polytope

A wheel in a graph G(V, E) is an induced subgraph consisting of an odd hole and an additional node connected to all nodes of the hole. In this paper, we study the wheels of the column intersection graph of the OLS polytope (PI). These structures induce valid inequalities for this polytope, which are facet defining for its set packing relaxation. Our work builds on simple structural properties of wheels which are used to categorise them into a number of collectively exhaustive classes. Each such class gives rise to a set of valid inequalities for PI . Moreover, this classification allows us to estimate the cardinality of the whole wheel class as well as to derive a recognition algorithm for the circulant matrices corresponding to wheels of a particular type. In a forthcoming paper, we show for some of the wheel classes presented here that they give rise to facet-defining inequalities for PI .