The branch-type conjecture for sufficiently large minimal-ABC trees

Let $n$ be the order of a minimal-ABC tree, and let big vertices denote the vertices distinguished as big in the paper's branch decomposition. The branches other than those incident with the big vertices are classified as $B_i$-branches.

Branch-type conjecture. For sufficiently large $n$, minimal-ABC trees have only $B_3$-branches besides the big vertices.

This is the second conjecture attributed by the paper to earlier work. The supplied text gives no resolution status, so it remains open in this database.