SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2270-2281, January 2020.
A biased graph is a pair $(G,\mathcal{B})$, where $G$ is a graph and $\mathcal{B}$ is a collection of “balanced” cycles of $G$ such that no $\Theta$-subgraph of $G$ contains precisely two balanced cycles. We prove a Ramsey-type theorem, showing that if $(G,\mathcal{B})$ is a biased graph for which $G$ is a very large complete graph, then $G$ contains a large complete subgraph $H$ such that the set of balanced cycles within $H$ has one of three specific, highly symmetric structures, all of which can be described naturally via group-labelings.

中文翻译：

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有偏图的Ramsey定理

SIAM离散数学杂志，第34卷，第4期，第2270-2281页，2020年1月。
有偏图是一对$（G，\ mathcal {B}）$，其中$ G $是图，而$ \ math { B} $是$ G $的“平衡”周期的集合，因此$ G $的$ \ Theta $子图不包含精确的两个平衡周期。我们证明了Ramsey型定理，表明如果$（G，\ mathcal {B}）$是一个有向图，而$ G $是一个非常大的完整图，则$ G $包含一个较大的完整子图$ H $因此，$ H $内的一组平衡环具有三个特定的高度对称结构之一，所有这些都可以通过组标记自然地描述。