To share or not to share your partner

In this day of sexual exploration and liberation, we find couples exploring with each other as well as with others or engaging in bisexual relationships. The question is, is there monogamy in bisexual relationships?  A case in point, a bisexual female gets together with a man then vows that she would give up her other relationship and be faithful to him. Is this really possible? Can a bisexual partner stick to one sex/gender completely and be faithful? Is this a relationship that someone seeking a faithful partner should get into and hope for the best?
Yes men cheat on their partners with other women or women cheat on their partners with other men but this would be a case where a bisexual has more options as they can go to either gender. So for someone who wants to be in a committed relationship and falls in love with a person who s bisexual, is there any hope that this would be a faithful relationship or marriage?
What are your views? I think that this is a difficult one, nevertheless I may be wrong but I cannot conceive that this would be a faithful relationship.
I have heard of cases where the bisexual women although involved with a man, still want to have their affairs on the side with their female lovers and do not consider it cheating as they are not involved with another man. Seriously? Regardless of the gender, if you are not committed to one person then you are cheating and need to decide who to settle with.

This is a short topic to write on, however, it is food for thought. Unless either partner does not mind, I don't think that there can be monogamy in a relationship with a bisexual and one should think very hard when getting involved with such person.