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We prove that, for sufficiently large $n$, every graph of order $n$ with minimum degree at least $0.852n$ has a fractional edge-decomposition into triangles. We do this by refining a method used by Dross to establish a bound of $0.9n$. By a result of Barber, K\"{u}hn, Lo and Osthus, our result implies that, for each $\epsilon >0$, every graph of sufficiently large order $n$ with minimum degree at least $(0.852+\epsilon)n$ has a triangle decomposition if and only if it satisfies the obvious necessary conditions.

On the Minimum Degree Required for a Triangle Decomposition