Single-pass streaming MVC in general graphs better than 2

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

Background

For general graphs, minimum vertex cover can be up to twice the maximum matching, and known streaming techniques have not achieved better-than-2 approximations in one pass with linear space.

Clarifying this would significantly advance the understanding of streaming complexity for general graph optimization problems.

References

The same holds true for surpassing a 2-approximation for Minimum Vertex Cover (MVC) in bipartite graphs, as well as the seemingly more challenging problem of approximating MVC on general graphs.

— One-way Communication Complexity of Minimum Vertex Cover in General Graphs (2505.00164 - Derakhshan et al., 30 Apr 2025) in Introduction, Relation to streaming algorithms