Deg(Ri) is defined as the number of the i-th face, that is, the boundary length of this face.

Then there must be ∑deg(Ri) = 2m (adding the boundary lengths of all faces is equivalent to the number of sides twice).

In this problem, ∑deg(Ri) > = 4k (because each face is surrounded by at least four sides).

So 2m & gt=4k, which means 2k.

According to Euler formula: n+k-m=2.

4 = 2n+2k-2m < =2n+m-2m=2n-m

That is m < =2n-4.