A mesh can be an example of a complete G. Where each node is connected to every other node. So shouldn't the minimum vertex cover size for such a graph is '1'.
A graph, G, has a minimum vertex cover of size |V| - 1 if and only if G is complete. Is it true?
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Minimum vertex cover is the set of vertices such that every edge is touching a vertex in the set. Given a mesh (complete graph) of
ABandC, if you only have one node (sayA) as your attempted MVC, you're missing an edge (in this case the edgeB-C).