what is the maximum number of faces with m edge and n vertex in planar graphs?

e=number of edges

v=number of vertices

f= number of faces

for example if v=3 -> max(f)=2

v=4 -> max(f)=4 (a triangle with a point in inner face of it , connected to the three vertex)

v=6-> max(f)=8


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  • $\begingroup$ what is meant by face? $\endgroup$ – Tomas Dec 28 '13 at 21:14

Euler's formula states

v − e + f = 2


f = 2 - v + e

So for given number of vertices and edges, the number of faces follows exactly.


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