An independent transversal (also called a rainbow-independent set" or independent system of representatives"') is a transversal which is also an independent set of a given graph. To explain the difference in figurative terms, consider a faculty with "m" departments, where the faculty dean wants to construct a committee of "m" members, one member per department. Such a committee is a transversal. But now, suppose that some faculty members dislike each other and do not agree to sit in the committee together. In this case, the committee must be an independent transversal, where the underlying graph describes the "dislike" relations.