We consider random perfect matchings on a general class of contracting bipartite graphs by letting certain edge weights be 0 on the contracting square-hexagon lattice in a periodic way. We obtain a deterministic limit shape in the scaling limit. The results can also be applied to prove the existence of multiple disconnected liquid regions for all the contracting square-hexagon lattices with certain edge weights, extending the results proved in [ 13] for contracting square-hexagon lattices where the number of square rows in each period is either 0 or 1.

中文翻译：

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收缩二部图上完美匹配的极限形状

我们通过周期性地让收缩方六边形格上的某些边权重为 0 来考虑一般类收缩二部图上的随机完美匹配。我们在缩放限制中获得了确定性的限制形状。该结果还可以用于证明所有具有一定边权的收缩方六边形格子存在多个不连通的液体区域，扩展了 [13] 中证明的收缩方六边形格子的结果，其中每个方格的行数周期为 0 或 1。