Largest common subtree for preferential attachment trees

Determine whether the largest common subtree size X_n for two independent preferential attachment trees satisfies X_n=n^{1-o(1)} with high probability.

Background

The paper extends some lower-bound techniques from uniform attachment to general attachment rules and obtains polynomial lower bounds under broad conditions. It also proves near-linear behavior for polynomially superlinear preferential attachment, but leaves the ordinary preferential attachment and other regimes unresolved.

The question asks whether the near-linear conjecture proposed for uniform attachment persists for preferential attachment.

References

For instance, how does $X_{n}$ grow for PA? Is it true that $X_{n} = n{1-o(1)}$ with high probability for PA?

— On the largest common subtree of uniform attachment trees  (2609.30098 - Bäumler et al., 24 Sep 2026) in Section 1, Subsection 1.3, item “General tree growth models”