Upper edge-connectivity bound for the rainbow disconnection number

Let $G$ be a connected graph. The upper edge-connectivity $\lambda^+(G)$ is the maximum local edge-connectivity of $G$, and $\operatorname{rd}(G)$ denotes the rainbow disconnection number of $G$.

Rainbow disconnection bound. The conjecture states

$$\lambda^+(G)\leq \operatorname{rd}(G)\leq \lambda^+(G)+1.$$

This conjecture extends the bound known for connected regular graphs, complete multipartite graphs, and grid graphs. The paper proves it for many classes of graphs, but the general case is presented as open.