Girlfriend admitted she went back to her ex

So a few months ago me and my girlfriend had an argument. We argued because she said something about her ex - she was confused about her feelings for him. So we stopped talking for a few weeks. Then she came back to me a few weeks ago. I asked no questions because I was happy... I thought everything was okay. But something similar happened again and I decided to confront her about it because I couldn't keep holding on to the doubts I had. So today she finally admitted that she went right back to her ex during the time me and her were on no contact. She even had sex with him and went to his house many times and he went to hers (she never invited me to her house before). So, I broke up with her and told her not to contact me again because it's not fair for me to have to deal with her past. I told her it's not okay to keep going back and fourth between two boyfriends and that's something I don't respect in a girl. I really liked this girl but she crossed the line. She told me she loves me and I believe it, but still, I know I deserve something better. Did I do the right thing? I followed my feelings because I know there is no way I would be able to live with the fact that she was with him while me and her had something going on.

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