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A bipartite graph is a graph whose vertices can be divided into two disjoint sets such that no two vertices in the same set are adjacent.

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Bipartite graph with exactly one perfect matching

$\textbf{Problem:}$ Find all bipartite graphs $G[X,Y]$ satisfying the following properties: $1.$ $|X|=|Y|$, where $|X|\ge 2$ and $|Y|\ge 2$. $2.$ All vertices have degree three except for two vertices …
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