Edge-maximal graphs without disjoint odd cycles

For a graph G we define ex(n, G) to be the maximum number of edges in a graph on n vertices that does not contain G as a sub-graph. Similarly, let ex'(n, G) be the largest number of edges in a Hamiltonian graph having n vertices which does not contain G. We study ex (n, G) and ex'(n, G) if G is the disjoint union of p >= 2 odd cycles. We present exact values of ex(n, G) and ex'(n, G) for sufficiently large n if G is the disjoint union of two cycles of order 2k + 1, where k >= 2.