The Erdős-Sós bipartite-link conjecture asserts that a 3-uniform hypergraph on 
vertices whose every vertex link is a bipartite graph
has at most 
edges as 
. The link of a vertex 
has the remaining vertices as its vertices and an edge 
precisely when 
is a hyperedge. This conjecture is distinct from the
Erdős-Sós theorem about trees in
graphs.
Yang (2026) constructed a counterexample with 497 vertices and 5115152 edges, all of whose vertex links are bipartite. Replacing each vertex by 
vertices and each hyperedge by all triples from the corresponding
three classes gives such hypergraphs on 
vertices with
 |
edges. Their limiting edge density is 
, strictly greater than 
. Yang (2026) reports using GPT-6.1 for strategies and proof
checks, with the results reviewed by the author.
