Chartrand et al.'s odd-order maximum-size conjecture for rainbow disconnection number

Let $G$ be a connected graph of order $n$, and let $rd(G)$ be its rainbow disconnection number, the minimum number of colors needed in an edge-coloring so that every pair of vertices is separated by a rainbow edge-cut. Let $k$ and $n$ be integers with $1\leq k\leq n-1$, and suppose that $n\geq 5$ is odd.

Chartrand et al.'s conjecture. The maximum size of a connected graph $G$ of order $n$ with $rd(G)=k$ is

$$\frac{(k+1)(n-1)}{2}.$$

This is the odd-order maximum-size question left by the earlier determination of the corresponding minimum size. The paper presents the result as a conjecture posed by Chartrand et al. and states elsewhere that it solves the conjecture.