I'm really struggling with the following proof.
Prove that if G is an n-vertex graph and δ(G) ≥ ⌊n/2⌋, then κ′(G) = δ(G).
My first thought was to construct a proof by contradiction, however, it seems that this may not be a good approach since I would have to evaluate κ′(G) $\neq$ δ(G). My second thought was to use proving the contrapositive: If κ′(G) $\neq$ δ(G), then δ(G) < ⌊n/2⌋. But again this involves evaluating when κ′(G) = δ(G). Is there a better way to go about this proof or are either of these sufficient and I'm overlooking something. Thanks