Question

The minimum numbers of colours required to colour the verticles of a cycle with n nodes in such a way that no two adjacent nodes have the same colour is

• A. 3
• B. $n-2\lfloor \frac{n}{2}\rfloor +2$
• C. 2
• D. 4

Answer 1

The correct option is B $n-2\lfloor \frac{n}{2}\rfloor +2$

The minimum numbers of colours require colour the vertices of a cycle with n nodes
= 2, when n is even
= 3, when n is odd
$Thereforen-2\lfloor \frac{n}{2}\rfloor +2$
gives 2 when n is even and 3 when n is odd.