We show that for every $\eta >0$ there exists $n_0$ such that for every odd $n\ge n_0$ each 3-colouring of edges of a graph G with $(4+\eta )n$ and minimum degree larger than $(7/2+2\eta )n$ leads to a monochromatic cycle of length n. This result is, up to η terms, best possible.

中文翻译：

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关于Schelp问题的三个奇长周期

我们证明了每个 $\eta >0$ 那里存在 ${ñ}_0$ 这样的每一奇 $ñ\ge {ñ}_0$的曲线图的边的每个3着色ģ与$（4+\eta ）ñ$ 最小度大于 $（7/2+2\eta ）ñ$导致长度为n的单色循环。在η项之内，此结果是最好的。