Ichihara's boundary slope diameter conjecture

Let $K$ be a knot in $S^3$. Denote by $D(K)$ the diameter of the set of boundary slopes of $K$, and by $c(K)$ its crossing number.

Ichihara's conjecture. For every knot $K$ in $S^3$,

$$D(K) \leq 2c(K).$$

The conjecture was proposed initially for Montesinos knots, a case later proved by Ichihara and Mizushima. The paper verifies it for $2$--bridge knots, where the boundary-slope diameter is twice the crossing number.