Scott–White multicolour pancyclicity conjecture

Let $n\geq 3$, let $k$ be an integer, and let $G$ be a graph of order $n$ with minimum degree

$$\delta(G)\geq\left(1-\frac{1}{2^k}\right)n.$$

A $k$-edge colouring is a decomposition

$$E(G)=\bigcup_{i=1}^kE(G_i),$$

where each $G_i$ is a spanning colour class. Scott–White's multicolour conjecture. Either, for every

$$\ell\in\left[\min\{2^k,3\},\left\lceil\frac{1}{2^{k-1}}n\right\rceil\right],$$

there is some $1\leq i\leq k$ such that $G_i$ contains $C_\ell$, or $n=2^kp$, $G$ is the complete $2^k$-partite graph with classes of order $p$, and the colouring is a $k$-bipartite $k$-edge colouring.

This conjecture extends the one-colour case of Bondy's theorem and the paper's two-colour result. The supplied text gives no resolution beyond noting these special cases, so its general status remains open.