Question: A perfect grid with m rows and n columns has edges connecting vertex such that each pair of neighboring vertices is connected by exactly one

A perfect grid with m rows and n columns has edges connecting vertex such that each pair of neighboring vertices is connected by exactly one road. What is the maximum number of edges that can be removed from the grid while still ensuring that all vertices are connected to each other?

Hint: to show a variable x has a maximum of M, you must first show that xM, and then provide an example where x is exactly equal to M.

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