Questionable behavior from a girl I've been dating. She's not ready to fully commit. What would you do?

Anonymous
I've been seeing a girl where we have been talking for less than 4 months. Just personal beliefs i mentioned to her that if we started sleeping together that i dont think we should sleep with anyone else. She agreed but also constantly talks about three main guys from her past.

One she dated for 4 years and the other two were recent flings. She is still in contact either text, social media, or in person with these people since one she works with, one goes to bars regularly where she goes, and the ex boyfriend she told me she had lunch with, when i confronted her about hanging out one on one with guys and tried to see where her level of exclusivity is. She is very wishy washy about the idea of committing to just me and letting them go.

i told her i can't control her actions and even if i did she would just do it behind my back. But ever since that conversation, about a week and a half ago, she would still bring up their names regularly. Make off taste comnents regarding our dating situation. I've made it very clear to her that im not interested in a friends with benefits type relationship and i feel like she is trying to make steps towards more commitment but the fact that she still talks to these guys without fully investing more into us is frustrating but something I've been trying to have patience with. It just really delays trust.

What I'm wondering is if it is possible to have a healthy relationship with this person? Also how long should i be "patient" with her actions or will she ever be emotionally and physically faithful to just one person because i get the feeling certain types of people just aren't capable of this.

I just dont think it's fair for me to have to wait on someone else while they take their time being committed but i also don't believe in rushing things

thanks for the advice or comments in advance
Questionable behavior from a girl I've been dating. She's not ready to fully commit. What would you do?
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