The degree-three threshold conjecture for leaf joined trees

Let $\Delta_0$ be the threshold parameter in Theorem~, concerning the accumulation of chromatic zeros of leaf joined trees relative to the degree bound $\Delta$. The degree-three threshold conjecture. Theorem~ remains true when

$$\Delta_0=3.$$

The conjecture is supported by numerical data for leaf joined trees and is related to questions on zeros of independence polynomials of bounded-degree graphs. The source provides no proof or resolution.