I have an $m \times n$ grid graph. I'm trying to find the maximum number of edges I can remove from the graph such that two vertices can still be connected in some roundabout way.
I know the total number of edges in a grid graph is $2mn - m - n$
I drew this out using a $2 \times 2$ grid and found I could only remove $1$ edge.
On a $3 \times 3$ grid, on a corner vertex, I can still only remove $1$ edge.
Is the maximum number of edges I can remove just $1$?