For all $k \geq 1$, give an example of an undirected graph that does not contain two disjoint odd cycles and it cannot be made bipartite by deleting k or fewer nodes. Prove that this graph has the required properties.
Hint: Consider an n × n grid graph for n > k. This graph is bipartite, now add a suitable set of edges to it, to get the required example.
I'm an absolute beginner in graph theory and I've no idea how to solve this problem, any help would be appreciated.