AI 中文总结
研究图完美匹配上的翻转动力学，通过用满足条件的装饰替换顶点得到装饰图族，证明了该族的一般上界，还针对团装饰和费舍尔装饰（平面图情形）得到更强界，且界与装饰大小无关。
AI 中文摘要
我们研究图的完美匹配上的翻转动力学，其中一次翻转是指沿着偶圈用互补的交替边替换完美匹配的边。特别地，我们想界定圈的最小长度，使得任意两个完美匹配可通过这种圈的翻转相互关联。给定有限图\(G\)，我们考虑通过用满足其子图中完美匹配存在的适当条件的装饰替换\(G\)的每个顶点而得到的装饰图族。我们证明了这个族的一个一般上界。然后对于两类装饰：团装饰和费舍尔装饰（后者在基础图是平面图的假设下），我们得到了更强的界。在这两种情况下，界都与装饰的大小无关。
英文摘要
We study the flip dynamics on perfect matchings of graphs, where a flip consists of replacing the edges of a perfect matching along an even cycle with the complementary alternating edges. In particular, we want to bound the minimum length of cycles such that any two perfect matchings are related by flips of such cycles. Given a finite graph $G$, we consider the families of decorated graphs obtained by replacing each vertex of $G$ with a decoration satisfying suitable conditions on the existence of perfect matchings in its subgraphs. We prove a general upper bound for this family. We then obtain stronger bounds for two families of decorations: clique decorations and Fisher decorations, the latter under the assumption that the underlying graph is planar. In both cases, the bounds are independent of the sizes of the decorations.
Comments19 pages, 10 figures
