Majority functions on structures with finite duality

A majority function is a ternary near-unanimity function. Dalmau and Krokhin have recently shown that the existence of a majority polymorphism on a relational structure is reflected in the complexity of the corresponding constraint satisfaction problem, implying that the problem has “bounded path duality”. Here we restrict our attention to core structures with finite duality. We completely characterise those among them which admit majority polymorphisms as those whose minimal obstructions are “caterpillars”.