Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.


share|cite|improve this question

1 Answer 1

up vote 2 down vote accepted

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

$$\forall (u,v) \in E. u \notin I \vee v \notin I$$

So as you can see a set is a vertex cover iff its complement is an independent set, and the converse also holds.

Therefore a minimal vertex cover $C$ corresponds to a maximal independent set $V-C$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.