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We provide a necessary condition for the existence of a 3-point holomorphicinterpolant $F:\mathbb{D}\longrightarrow\Omega_n$, $n\geq 2$. Our condition isinequivalent to the necessary conditions hitherto known for this problem. Thecondition generically involves a single inequality and is reminiscent of theSchwarz lemma. We combine some of the ideas and techniques used in our resulton the $\mathcal{O}(\mathbb{D},\Omega_n)$-interpolation problem to establish aSchwarz lemma -- which may be of independent interest -- for holomorphiccorrespondences from $\mathbb{D}$ to a general planar domain $\Omega\Subset\mathbb{C}$.

The 3-point spectral Pick interpolation problem and an application to holomorphic correspondences