SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 597-610, January 2020.
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 [SIAM J. Discrete Math., 30 (2016), pp. 36--42] to establish a bound of $0.9n$. By a result of Barber, Kühn, Lo, and Osthus [Adv. Math., 288 (2016), pp. 337--385], 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 has all even degrees and number of edges a multiple of three.

中文翻译：

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关于三角形分解所需的最小度

SIAM离散数学杂志，第34卷，第1期，第597-610页，2020年1月。
我们证明，对于足够大的$ n $，最小度至少为$ 8.552n $的每张图$ n $都具有分数边-分解为三角形。我们通过完善Dross [SIAM J.Discrete Math。，30（2016），pp.36--42]来建立$ 0.9n $的界限的方法来做到这一点。由Barber，Kühn，Lo和Osthus的结果[Adv。Math。，288（2016），pp。337--385]，我们的结果表明，对于每个$ε> 0 $，每个具有最大阶且最小度至少为（$ 0.852 + \ epsilon）的图）n $当且仅当其所有偶数度和边数均为3的倍数时，才进行三角形分解。