Corporate jet Captain reported a ground conflict with a general aviation aircraft after clearing the runway for taxi. The Captain immediately applied the brakes as the other aircraft veered to avoid a collision.

Narrative

We conducted an unplanned visual approach to Runway XXL (5;000 Feet Long) at ZZZ. The approach and landing were uneventful. We exited the runway; to the right; on Taxiway 1. When clearing the runway; the size of the Falcon took up more than half of Taxiway 1 to get the airplane's tail completely clear of the runway. After about 15 seconds of radio chatter; we reached Ground Control; and they cleared us to taxi west on 1; to 2; to 3 for the ramp. As I released my toe brakes; I looked to my left (east) and a Cessna 172 was taxiing toward me on 1 at a high rate of speed. He veered south to avoid collision and turned onto the connecting taxiway across from 1. I immediately applied brakes and we reported the incident to the ZZZ Tower. Sadly; they did not acknowledge or clarify the Cessna's clearance. We continued our taxi to the Ramp without further incident. I called the Control Tower by telephone to discuss the event. They said they were not aware of his taxi west on 1 and were going to review security footage. They did verify the operator's tail number and said it was a tour operator and they were notorious for taxiing extremely fast as they are charging flat rates for tours. The Tower Controller said he would contact the tour operator management to stress normal taxi speeds to allow time for pilot reaction should something go wrong.