Bogdanov–Neustroeva–Sokolov–Volostnov–Russkin–Voronov conjecture for bipartite cuts

Let $G$ be an $n$-vertex graph. A bipartite cut is a cut whose induced subgraph on one side is bipartite. Bogdanov–Neustroeva–Sokolov–Volostnov–Russkin–Voronov conjecture. Any $n$-vertex graph with fewer than $3n-6$ edges admits a bipartite cut, while some graphs with $3n-6$ edges do not. In particular, $\ell_3=3$. This is the next case after the resolved case $\ell_2=2$; the conjecture is open, with partial progress on related forest-cut and bipartite-cut bounds.