Fractional Nash-Williams' conjecture

Let $G$ be a graph on $n$ vertices. A fractional $K_3$-decomposition assigns a non-negative weight to each triangle of $G$ so that the sum of the weights over the triangles containing each edge is exactly one.

Fractional Nash-Williams' conjecture. If

$$\delta(G) \geq \frac{3}{4}n,$$

then $G$ admits a fractional $K_3$-decomposition.

The fractional statement is a relaxation of Nash-Williams' conjecture and is used to obtain integral decompositions above the relevant threshold. The paper's context says that this conjecture is proved in the paper, so its status is recorded as solved.