Definition (Perfect Matching). Given a graph $\mathcal{G} = (E,V)$, then a Perfect Matching $M$ is a set of pair-wise non-adjacent edges from $E$, such that every vertex in $V$ is touched by one edge in $M$.
Here is a little example for a two PMs in a graph:
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| Figure 1 - Top: The original graph $\mathcal{G}$; Below: The red lines indicate two example perfect matchings in $\mathcal{G}$ |
This post list some of the properties of PMs regarding finding and counting them in different graphs types. During writing this posts, i found that a similar listing can also be red in [6].
