Bondy–Erdős conjecture for multicolour Ramsey numbers of odd cycles

Let $k\geq 2$ and let $n>3$ be odd. Write $R_k(C_n)$ for the least integer $N$ such that every colouring of the edges of the complete graph $K_N$ with $k$ colours contains a monochromatic cycle $C_n$. Bondy–Erdős conjecture.

$$R_k(C_n)=2^{k-1}(n-1)+1.$$

This conjecture concerns the exact determination of multicolour Ramsey numbers for odd cycles, a class for which exact results were previously known mainly in the two-colour case. The paper addresses the conjecture; the supplied text gives no resolution status.