What is the minimum number of seismic monitoring centers needed to provide the data for triangulation?

3

Explanation:

The answer is within the question since it talks about triangulation a triangle.

The principle is that from each station, you get a distance location from that station of the event. Then from each center you make a circle with the distance measured at that center.

All three circles done form the monitoring centers will meet at a point somewhere between those three centers, and you'll get your location.

That's the triangulation process.  You do need 3 points for a precise reference, if you have only 2, you are left with 2 possibilities.