Is there a connected infinite graph $G=(V,E)$ such that $\text{deg}(v) \geq 2$ for all $v\in V$, and $G$ possesses no perfect matching?
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asked Dec 1, 2017 at 9:45
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What did you try? $K_{32}$ has no perfect matching. So start with any infinite connected graph with minimum degree $2$, pick two vertices $u,v$ and add three new vertices $A,B,C$ each of degree $2$ with edges going to $u$ and $v.$ No matching can have edges on all three of the new vertices.
answered Dec 1, 2017 at 10:09
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$\begingroup$ I agree it's a bad question. Let's delete / close it. $\endgroup$ Commented Dec 1, 2017 at 14:14