Inductive freeness of free connected subgraph arrangements

Prove that a connected subgraph arrangement is free if and only if it is inductively free.

Background

The paper recalls the classification of free connected subgraph arrangements and notes that computational evidence through rank 8 suggests that every free arrangement in this class is inductively free. Since inductive freeness is a stronger property than freeness, the conjecture seeks to establish equality of these two classes for connected subgraph arrangements.