Let $n\in\mathbb{N}$ be a positive integer and let $G =(V,E)$ be a connected simple undirected graph with $|V| = 2n$. Is it true that if for the minimal degree $\delta(G)$ we have $\delta(G) \geq n$, then $G$ has a perfect matching?



Matching and minimal degree
Yes. This question was asked before, for example [here](https://math.stackexchange.com/questions/56063/minimum-degree-of-a-graph-and-existence-of-perfect-matching "Math StackExchange"), where you can find various proofs of your claim.


For example, the condition of connectedness follows from $\delta(G) \geq n$. The claim is then an application of [Dirac's Theorem](https://en.wikipedia.org/wiki/Hamiltonian_path#Bondy.E2.80.93Chv.C3.A1tal_theorem "Wikipedia").


