The covering radius of the cycle code of a graph

AbstractThe cycle code of a graph is the binary linear span of the characteristic vectors of circuits. We exploit a connection between the covering radius of this code and minimum T-joins. We obtain a lower bound on the covering radius which is met with equality when the graph is Hamiltonian or is regular and has edge connectivity equal to its degree. We also solve several other examples and we note some cycle codes which are optimal for the covering problem