GATE | GATE-CS-2016 (Set 2) | Question 13

The minimum number of colours that is sufficient to vertex-colour any planar graph is _______________

[This Question was originally a Fill-in-the-blanks Question]
(A) 1
(B) 2
(C) 3
(D) 4


Answer: (D)

Explanation: A planar graph is a graph on a plane where no two edges are crossing each other.

The set of regions of a map can be represented more abstractly as an undirected graph that has a vertex for each region and an edge for every pair of regions that share a boundary segment. Hence the four color theorem is applied here.

Here is a property of a planar graph that a planar graph does not require more than 4 colors to color its vertices such that no two vertices have same color. This is known four color theorem.


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