[en] We study boundary operators (open string vertices) in two-dimensional gravity and identify them as redundant operators in the matrix model. In the (p, q) minimal model coupled to 2D gravity there is always one relevant boundary operator, which measures the ζ₂-odd or ζ₂-even boundary length depending on whether q is odd or even. Our analysis also leads to new operators which exist in Liouville theory and in the matrix model but are not obvious in the KP description nor in the topological interpretation of these theories. (orig.)