Square of a cycle
= Square of a cycle
{title2=$C_k^2$}
= Cycle square
{synonym}
In a cycle square, each triple of consecutive <vertices> is a <clique>. A proper three-colouring therefore repeats with period three and closes exactly when the length is divisible by three. For all other cycle lengths at least four colours are needed; the five-cycle square is a complete five-vertex <graph>.