I know that not all bipartite graphs have perfect matching, but I am having trouble coming up with an example (I'm a visual learner). Can someone give me a visual example of a bi[artite graph without perfect matching?
2026-03-27 18:23:41.1774635821
Does a bipartite graph without perfect matching exist?
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Take a chain graph with 3 vertices and 2 edges:
$$ \bullet - \circ - \bullet $$
If you use the left edge, then you cannot use the right one (because you cannot use the white vertex twice), and similarly if you use the right edge, then you cannot use the left edge. Either way, a black vertex will be left unmatched.