doubt

Question

someone post complete solution

Answer 1

Option b) is correct

In a simple bipartite planar graph, degree of each region is at least 4, since v>=3 there is no cycle of length 3 

From Handshaking Lemma, we can write

$4|R|<=2|E| $

$|R|<=\frac{|E|}{2}$

From Euler Formula

$|V| + |R| = |E| + 2$

Substitute value of $|R|$ in above equation

$|E|-|V|+2<=\frac{|E|}{2}$

$|V|>=\frac{|E|}{2}+2$

$|E|<=2|V|-4$

Comments

Yeah answer is right but I am not able to digest this "4R <= 2E " could you please throw some light how did you get this?

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We know $\sum degree \ of \ region= 2*Edges$

Here degree of each vertex is at least 4 so

$4*|R| <= 2*|E|$