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Given a tropical divisor $D$ in the intersection of two tropical planecurves, we study when it can be realized as the tropicalization of theintersection of two algebraic curves, and give a sufficient condition. We showthat under a certain condition involving a graph determined by these tropicalcurves, we can algorithmically find algebraic curves such that thetropicalization of their intersection is $D$.

Tropical lifting problem for the intersection of plane curves