holds that honesty is one of the major virtues. In the end, one gains nothing by dishonesty; it leaves one trapped in a web of fakery, which makes reality one's enemy and reason a threat to be feared in anybody one knows.
Objectivism also holds that integrity is a major virtue. One should look to the long-term and the full range of consequences, and act steadfastly in accordance with rational principles and rational commitments that one has made.
For these reasons, Objectivism holds that one should be honest in relationships, especially with a lover. "Cheating," as it is normally thought of, involves hiding what one is doing or sneaking around. Objectivist principles imply that if one is (or is going to be) involved with someone besides one's committed partner, one should be honest with all parties concerned. Love is premised on knowledge: What the lover does not know, he cannot love.
Similarly, if one makes a serious commitment to an exclusive relationship, such as a marriage, then as a matter of integrity one should hold true to the values implicit in that commitment. One should neither make such commitments lightly, nor should one break them lightly.
However, to put all this in a broader context, note that Objectivist morality is value-centered. It is not a system of rules or duties, but a set of principles for the sake of achieving a happy life. Serious contracts like marriage are means of gaining values. They have worth only because they enhance our lives and bring us happiness. The commitment to a relationship is therefore worth no more than the relationship itself.
But for the same reason, one's degree of commitment to a relationship should accord with the degree of value one places on it. If a couple are dating, and seem to be in love, yet one partner fools around with others on the side, this may be a sign that he does not value the relationship as much as he seemed to, or that he lacks integrity towards the things he loves.
As a value-oriented ethic, Objectivism as such is neither for or against exclusivity in relationships; it does not prescribe a form of dating; it does not favor or oppose marriage as an institution. It favors serious commitment to one's values, and honesty toward oneself and toward others in relationships.
In any particular relationship, to apply these principles, we would need to know: Did both parties share an exclusive commitment to the relationship? Did both parties understand the value that an exclusive commitment represented? (This is pretty obvious in the case of a married couple, but what about casual daters? Is exclusivity even implied there?) And in this context, was anyone dishonest about his actions, goals, or values? And did everyone pursue his long-term commitments consistently and rationally?