ABSTRACT The celebrated Andrásfai–Erdős–Sós theorem from 1974 shows that every ‐vertex triangle‐free graph with minimum degree greater than must be bipartite. We establish a positive codegree extension of this result for the ‐uniform generalized triangle : For every , if is an ‐vertex ‐free ‐uniform hypergraph in which each ‐tuple of vertices is contained in either zero edges or more than edges of , then is ‐partite. This result provides the first tight positive codegree Andrásfai–Erdős–Sós type theorem for hypergraphs. It also immediately implies that the positive codegree Turán number of is for all . Additionally, for , our result answers one of the questions posed by Hou et al. in a strong form.
Liu et al. (Sun,) studied this question.