Jung's reverse minimum-degree conjecture for long cycles

Let $G$ be a graph with minimum degree $\Greekmath 010E$ and connectivity $\Greekmath 0114$, where $1\leq\Greekmath 0114 \leq\Greekmath 010E$. Let $C$ be a longest cycle in $G$, and let $\overline{p}$ be the order of a longest path in $G-C$.

Jung's reverse minimum-degree conjecture. If $\overline{p}\geq\Greekmath 0114 -1$, then

$$c\geq\Greekmath 0114 (\Greekmath 010E -\Greekmath 0114 +2).$$

This is the minimum-degree reverse analogue of Bondy's conjecture. The paper presents the minimum-degree versions as popular and much-studied statements that remain unsolved.