Whether or not this is prohibited depends on where you live. In the United States, almost certainly yes (+1 to Nicole Hamilton for her answer).

My own personal belief is that what you propose is wrong, whether or not it is illegal where you work. It also demonstrates an misunderstanding of how people's relationships affect their work ethic. It has *not* been my personal observation that single people outwork those in relationships on average. Indeed, I know people (both men and women) who are not only married but also actively raising young children, and who work incredibly hard in their discipline.

You *may* choose to take only those students who demonstrate talent, hard work, and/or drive. I recommend that you do your best to judge these traits directly, rather than by how they conduct their personal lives.