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M. In particular show that |S Show that if M is a matching and S is some vertex cover max{IM| M is a matching of G} < min{|S|

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Answer #1

Soln :

Since each edge in M are disjoint, to cover all the edges in M we need at least |M| no of vertices ( one end-point of each edge).still If some vertex of the graph is uncovered ( i.e if M is not a perfect matching ) ,then S contains more vertices.

So in general , |S| ≥ |M|.

In particular, max |M| ≤ min |S|

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