Made easy test

Question

Let G be a planar graph such that every face is bounded by exactly three edges. What are the possible values for chrmatic number of G?

a) 3 or 4

b)only 4

c)only 3

d) none

Answer 1

It may be both 3 and 4.

We may verify this by using K₃ and K₄ complete graphs both of which are also planar.

Also both of them contains cycle size 3 only so each face of both of them is bounded by 3 sides.

In K₃  as we know chromatic number is 3 and K₄ has chromatic number 4.

Hence A) should be the correct option.