I am working on an exercise describe like so:
Without using knowledge about cliques, prove that a graph G has an independent set of size k if and only if G has a vertex cover of size n - k where n is the size of V, the vertex set of G.
I am attempting to write a proof for this and was hoping for help with the concept and wording.
By definition of independent sets, the complement of independent set of size k will result in every vertex being connected by an edge to form a maximum clique size of n - k.
Is this sufficient enough or how should I add to it to make it concrete?