Mihawk ended this debate when he spoke about the Swordsman's Code in his fight against Zoro.
King vs Zoro put the nail in the coffin, for those who still tried to argue that there was no such thing, despite Mihawk mentioning it.
We've pretty much got the whole picture now. When Zoro flashbacked to Kozaburo, Kozaburo made mention that Swords were made for killing.
In Zoro's fight against King, when King attacked with his Sword, and then went for a punch while Zoro was unguarded, Zoro said he was just "A Killing Machine.", to which King answered you don't need a school or style in order to fight. Zoro responded with nope, good point, and you never called yourself a Swordsman.
Someone who uses a Sword only to kill, and doesn't use any kind of style or follows the Swordsman's code, is not a Swordsman.