A Counterexample to the Bernhard–Jablan Unknotting Conjecture. Issue 4 (1st December 2021) - Brittenham, Mark; Hermiller, Susan
Abstract: We show that there is a knot satisfying the property that for each minimal crossing number diagram of the knot and each single crossing of the diagram, changing the crossing results in a diagram for a knot whose unknotting number is at least that of the original knot, thus giving a counterexample to the Bernhard–Jablan Conjecture.