So I'm a little desperate at this point. I've drawn like 5 pages of pictures and I just cant seem to see a pattern. Any insight would be awesome.
The problem:
Eulerize a grid graph G(m,n) for all m, n greater than or equal to 2.
...in other words, what is the fewest number of edges you need to duplicate so that the new graph has an Eulerian circuit.
G(3,3)
OOO

OOO = 4 added edges to make circuit

OOO
....sorry cant make grid graphs very well on a computer