Abstract
AbstractWe prove that the number of perfect matchings in is asymptotically normal when is even, as , and . This is the first distributional result of spanning subgraphs of when . Moreover, we prove that and can be coupled so that is a subgraph of with high probability when and . Furthermore, if , , and then and can be coupled so that asymptotically almost surely (a.a.s.) is a subgraph of .
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