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

Question

Accepted Answer

4 The Four Colour Theorem, proved in 1976 by Appel and Haken, states that every planar graph can be properly vertex-coloured with at most 4 colours. This is tight: there exist planar graphs (like K_4) that require exactly 4 colours. So 4 is both sufficient and the smallest such universal bound.