A reciprical relationship in which a person is paired with single other person. There are two possibilities: The trick, of course, is to tell one from the other, decide whether either is for you and then find an unsuspecting victim.

Unlike the polyamory/polygamy dichotomy (which arose for essentially legal reasons), the term monogamy covers both the legal state of being married to a single person and being in love with a single person. (Just a moment, … married to a single person … ? reparse that sentence the other way)

It is important not to confuse monogamy with monogramy, which is art, industry and fetish orientation of applying monograms. Monogamy is forever and monograms are damned hard to unpick, so this is not a mistake you want to make.