chromatic number

Question

Let G be a planar Graph Such that every phase is bordered by exactly 3 edges which of the following can never be value for X(G)

 a)2  b)3 C)4 d)none of these

Comments

Let G be a planar Graph Such that every phase is bordered by exactly 3 edges

since graph conain odd length cycle, its chromatic no. X(G)>=3

so 2 can never be X(G), hence option a is correct.

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Yes option a) is correct 2 is not possible because when a region consist exactly 3 edges means vertices joining them are adjacent and should be colored uniquely. You can also observe this with example below

 

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$\chi (G) \leq \Delta (G) + 1$