Characterization of all strongly regular graphs of VC-dimension two

Characterize all strongly regular graphs with VC-dimension exactly 2, without restricting the order of the graphs.

Background

The paper proves that for primitive strongly regular graphs of order at least 6401, VC-dimension 2 is equivalent to the complement having parameter \bar\mu=1. The authors explicitly ask whether a version of this characterization can be established without any lower bound on the order.

References

Solutions to the following problems would probably be more difficult to obtain, and would substantially improve on our results. Firstly, we ask whether a version of Theorem \ref{Theorem VC=2} can be proved with no restriction on $v$. Characterize all strongly regular graphs with VC-dimension exactly 2.

— The VC-dimension of strongly regular graphs  (2609.10330 - Byrne et al., 9 Sep 2026) in Section 8, Conclusion