Covering odd cycles (Q1272187)

If, in a graph, the number of vertices is \(n\), the length of the shortest odd cycle is \(g\), then the odd circuits can be covered by \(O({n \over g}\log({n \over g}))\) vertices and can also be covered by \(O(n^2/g^2)\) edges. The results, which are optimal, sharpen former estimates of Bollobás, Erdős, Simonovits, and Szemerédi.