A Min-max Relation for K3-covers in Graphs Noncontractible to K5e

In Euler and Mahjoub (1991) it is proved that the triangle-free subgraph polytope of a graph noncontractible to K,\e is completely described by the trivial inequalities and the so-called triangle and odd wheel inequalities. In this paper we show that the system defined by those inequalities is TDI for a subclass of that class of graphs. As a consequence we obtain the following min-max relation: If G is a graph noncontractible to K,\e, then the minimum number of edges covering all the triangles of G equals the maximum profit of a partition of the edge set of G into edges, triangles and odd wheels. Here the profit of an edge is 0, the profit of a triangle is 1 and the profit of a 2k + l-wheel (k E FV) is equal to k + 1.