Jackson–Tanigawa conjecture on the generic 2-hyperconnectivity matroid

Establish whether the generic 2-hyperconnectivity matroid is the freest among graph matroids in which every copy of K_4 and K_{3,3} is a circuit.

Background

The paper proves that every linearly representable abstract 2-rigidity matroid in which every K_{3,3} is a circuit has a two-dimensional hyperconnectivity-matrix representation. Consequently, any counterexample to the Jackson–Tanigawa conjecture that has full relevant rank must be nonrepresentable. The theorem therefore narrows the possible counterexamples but does not settle the conjecture for all graph matroids.

The conjecture compares the generic 2-hyperconnectivity matroid with the broader class of graph matroids satisfying the K_4- and K_{3,3}-circuit conditions.

References

A conjecture of Jackson and Tanigawa states that the generic $2$-hyperconnectivity matroid is the freest among graph matroids in which every $K_4$ and $K_{3,3}$ are circuits.

— Linear matroid products: a synthetic approach  (2609.16747 - Tyomkyn, 15 Sep 2026) in Section 1, Introduction, paragraph following Theorem 3 (Theorem~\ref{thm:main-hyper-realization})