The term "great sword" itself is a little vague, being simply a literal translation of the Scottish phrase claidheamh mór or "claymore" into English. However, generally this is referring to a sword that, by definition, requires two hands to wield it. Common examples are the German Zweihander, the Spanish Montante, or the Italian Spadone. Generally these are larger than what are modernly called "longswords" which are smaller and mostly two-handed but can still be wielded in one hand when necessary.

First, my sources. Dr. Ken Mondschein's "Art of the Two-handed Sword" delves into the use of these swords with a heavy focus on the Italian traditions, which are well-documented in several illustrated manuals of the 16th and 17th century. These manuals include Achille Marozzo's Opera Nova, Francesco Alfieri's Il Spadone, and Giacomo Di Grassi's His True Arte of Defense (originally published in Italian).

These manuals all emphasize moves using both hands, as these swords were fairly heavy, between 5 and 8 pounds. These weapons were primary used as an "area-control" weapon, with wide, sweeping cuts to keep the enemy back. For this reason they were sometimes used by bodyguards. These sweeping cuts can be done with one hand, but they are considerably slower and doing so is exhausting to even someone with above average strength. They would be so slow in most cases that an observant enemy could simply wait for the sword to pass, then dash it for an attack, safe from counterattack.

That said, di Grassi actually suggests using the sword one handed for thrusting, as shown in this illustration: https://wiktenauer.com/wiki/Giacomo_di_Grassi#/media/File:Di_Grassi_21.jpg

It is important to note though that this is not per se true one-handed wielding, because the action he describes involves holding the sword in both hands, starting the thrust motion and then releasing one hand, extending the other arm out and getting the maximum possible reach. This action contains some element of surprise as the enemy might think they are just out of range, and learn the hard way they are not. This is essentially using the great sword as a spear. However this is fairly limited and would not be possible with a shield in the other hand unless it was a strapped shield that left one hand free (which also leaves that hand vulnerable).

Using a great sword entirely one-handed would not make much sense since there are plenty of one-handed sword styles that are better suited to this. A sword's size and length are a balancing act after all, and usually a fighter will want a sword that meets there specific needs in terms of strength, mobility, armor, and fighting style, rather than just wanting the biggest they can swing.

Very long swords that are not great swords did exist. For example, there are some rapiers that were 4.5 feet long. The thin blade mean a weapon that only weighs 3.5 pounds, making using them one handed much more viable. However, how you fight with this weapon would be very different from a great sword.