The three-\B_1-branch conjecture for minimal-ABC trees

Let a minimal-ABC tree be a tree minimizing the atom-bond connectivity index among trees of the relevant order, and let a $B_1$-branch denote the branch type used in the paper's classification of such trees.

Three-$B_1$-branch conjecture. A minimal-ABC tree can contain at most three $B_1$-branches.

The paper notes that this improves the proved upper bound of four and is close to the conjectured sharp bound. It is known to be attained by minimal-ABC trees with $14$ and $19$ vertices, while the general assertion remains open in the source.