The Turán Number of Berge Paths

ABSTRACT A Berge path of length in an ‐uniform hypergraph is a collection of hyperedges and vertices such that for each . Győri, Katona, and Lemons generalized the Erdős–Gallai theorem to Berge paths and established bounds for the Turán number of Berge paths. However, these bounds are sharp only when certain divisibility conditions hold. Győri, Lemons, Salia, and Zamora determined the exact value of the Turán number of Berge paths in the case . In this paper, we settle the final open case , thereby completing the determination of the Turán number of Berge paths.