A committed
relationship is an interpersonal
relationship based upon a mutually agreed-upon commitment to one another involving love, trust, honesty, openness, or some other agreed-upon behavior
The act of being in a
relationship with someone and being monogamous.
Terms related to committed relationship include:
monogamy: having a single long-term sexual partner
sexual fidelity: not having other sexual partners other than one's committed partner, even temporarily