... why not just use a really big calvary saber?(Not a lightsaber of course since they don't curve)
Big weapons are made to be two handed, and unless its a bastard sword, I don't think they've ever been used for mounted combat... at least, not effectively.
A saber is shaped to add to the momentum already added by your mount and is meant to be swung with one hand while the other controls the animal. The reason people don't use claymores on horses... is because its illogical. True you have a dragon who might be strong enough to keep you on, but why risk it? A big sword can be a big hindrance so why use it? Use the weapons designed for the attack, not the one that looks cool.