We know that "If every node of a bipartite graph has the same degree $d\geq 1$, then it contains a perfect matching".
What if every node has degree $\geq k$ ($k$ a positive number), does the graph still continues to have perfect matching ?
2026-02-22 19:26:15.1771788375
Perfect Matching
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No, because with only that assumption you're not guaranteed that there are equally many vertices in each of the two parts of the graph. And if the two parts do not contain equally many vertices, then a perfect matching is impossible.