Can she do this? Use her feelings as justification to tell me who I can talk to?

My girlfriend now of a few years is asking me to remove friends from facebook and stop talking to friends I made during a semester abroad that we both took together. During the trip, I was very immature and frequently got intoxicated and was a real jerk a lot times. I even went so far as to cheat on her. This was about a year ago and since then, we broke up for about 9 months. I took that 9 months time to gather myself, get all the partying and drinking out of my system, and I approached her when I felt I was ready to be in a serious relationship (3 months ago), because clearly I was not ready before.

Well, the last 3 months went pretty well except she is very deeply hurt from my actions on our trip, and rightfully so. Our biggest problem now is that I still keep in contact with some friends from my trip and that deeply bothers her. She says that when I talk to these people it reminds her of the past. I understand this but I concede that it is not right for her to tell me who to talk to or not. I take it upon myself to not associate with any of the people I hooked up with in the past, and my friends really had nothing to do with me being a jerk, aside from the fact that they were on the trip too. So now we are on the verge of breaking up over this issue. I am trying to find a compromise but she is unwilling to budge, what do I do? On one hand I want to be with her, but I don't think it's right for her to tell me who I can talk to.