Single-pass streaming MVC in bipartite graphs better than 2

Determine whether there exists a one-pass streaming algorithm using O(n) space that computes a minimum vertex cover in bipartite graphs with approximation ratio strictly less than 2.

Background

Due to König’s theorem, maximum matching and minimum vertex cover coincide in bipartite graphs, yet existing streaming techniques do not directly yield a vertex cover approximation below 2 using a single pass and linear space.

This remains unresolved, indicating a gap between matching approximations and vertex cover construction in the streaming setting.