Girth-forces-dense-bipartite-induced-subgraph conjecture

Let $d_0$ and $g_0$ be constants. A bipartite induced subgraph is an induced subgraph that is bipartite. Girth-induced-subgraph conjecture. There exist $d_0$ and $g_0$ such that any graph of girth at least $g_0$ with minimum degree at least $d_0$ contains a bipartite induced subgraph of minimum degree at least $3$. This is a high-girth specialization of the search for dense bipartite induced subgraphs in graphs of large minimum degree. The supplied text gives no resolution.