A character who's main tool for fighting is a sword. It can get complemented/supplemented by haki or df or science.
Worth Mentioning:
Ryuma - Swordsman (self-explanatory)
Mihawk - Swordsman (self-explanatory)
Zoro - Swordsman (self-explanatory)
Oden - Swordsman (self-explanatory)
Roger - Swordsman (self-explanatory until proven otherwise)
Shanks - Swordsman (self-explanatory until proven otherwise)
Rayleigh - Swordsman (self-explanatory until proven otherwise)
Fujitora - Swordsman (always uses his sword together with his DF even when he was just lifting rubbles)
Law - Swordsman (most of his skills he needs his sword for cutting whether it is internal destruction technique or he is cutting in his rooms)
King - Not Swordsman (Most of his named attacks are from when he is in DF/Hybrid form and doesn't use sword. Iirc he has only one named attack while using his sword which is the flame dragon. Correct me if I'm wrong, I haven't had the time to re-read his fight with Zoro.)