5. we say that a set of vertices a ⊆ v is a vertex cover if every edge of the graph is incident to a vertex in the cover (so a vertex cover covers the edges). since v itself is a vertex cover, every graph has a vertex cover. the interesting is about finding a minimal vertex cover, one that uses the fewest possible number of vertices.
a). suppose you had a matching of a graph. how can you use that to get a minimal vertex cover? will your method always work?
b.) suppose you had a minimal vertex cover for a graph. how can you use that to get a partial matching? will your method always work?
c). what is the relationship between the size of the minimal vertex cover and the size of the maximal partial matching in a graph?