# Vertex Cover Problem

How to show that in every graph, the minimum size of a vertex cover is equal to number of vertices minus the maximum size of an independent set.

According to Vertex cover two problem are not equivalent, but there are should be kind of connection between them.

Thanks!

A subset $C \subseteq V$ is a vertex cover iff
$$\forall (u,v) \in E. u \in C \vee v \in C$$
A subset $I \subseteq V$ is an independent set iff
$$\forall (u,v) \in E. u \notin I \vee v \notin I$$
Therefore a minimal vertex cover $C$ corresponds to a maximal independent set $V-C$.