Mathematics, 20.08.2019 23:30 ringo12384

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?

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5. we say that a set of vertices a ⊆ v is a vertex cover if every edge of the graph is incident to a...