Which glacial period's end flooded the Black Sea basin, per one hypothesis?

The last ice age. Two Columbia geologists proposed in 1997 that the Black Sea had been a freshwater lake far below sea level, and that as glaciers melted the Mediterranean rose until it broke through the Bosphorus around 5600 BC - a torrent they estimated at two hundred times the flow of Niagara, raising the lake fifteen centimetres a day and drowning tens of thousands of square kilometres.

They connected it to the flood myths, which is why anyone outside geology heard about it. Displaced farmers would have carried the story outward, and the Mesopotamian and biblical accounts descend from it - a neat suggestion that made the book sell and made the hypothesis famous well beyond its evidence.

It has not held up well. Later coring suggests the water level was much less far down, that the connection may have been gradual over centuries or even flowed the other way, and that shells taken as evidence of a sudden saltwater arrival can be read differently. There is no doubt the basin did change from fresh to salt as sea level rose; whether it happened catastrophically is the disputed part, and the flood-myth link rests on the catastrophic version.