Dunbar-Haynes-Teschner-Volkmann planar bondage-number conjecture

Let $G$ be a planar graph, and let $\Delta(G)$ denote its maximum vertex degree and $b(G)$ its bondage number, the smallest number of edges whose removal increases the domination number. Dunbar-Haynes-Teschner-Volkmann conjecture. If $G$ is a planar graph then we have

$$b(G)\leq \Delta(G)+1.$$

This is one of two stated upper-bound conjectures for the bondage number, and the source identifies these conjectures as still open.