The minimum number of colours that is sufficient to vertex-colour any planar graph is …
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GATE CSE 2016 Set 2 · Q3
NAT1 markEasy
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The minimum number of colours that is sufficient to vertex-colour any planar graph is ________.
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Official answer: 4
Graph TheoryBy the Four Colour Theorem (proven by Appel and Haken in 1976), any planar graph can be vertex-coloured using at most colours such that no two adjacent vertices share the same colour.
Since a complete planar graph requires at least colours, fewer than colours are not sufficient for every planar graph.
Hence, the minimum number of colours sufficient to vertex-colour any planar graph is 4.
Try the question first, then check your work.
Examiner trap
The misconception this question tests
Recall the famous Four Colour Theorem for planar graphs.
This Graph Theory previous year question is Q3 of the GATE CSE 2016 Set 2 paper. Find more GATE CSE PYQs on Graph Theory in Engineering Mathematics, or browse all GATE CSE PYQs.
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Graph Theory in GATE CSE
Graph Theory has 21 GATE CSE PYQs across 14 papers from 2012 to 2026. 3 of them are 1-mark NAT questions like this one, and it is the only one in GATE CSE 2016 Set 2.
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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.