I need to reduce the vertex cover problem to a SAT problem, or rather tell whether a vertex cover of size k exists for a given graph, after solving with a SAT solver. I know how to reduce a 3-SAT problem to vertex cover problem, by constructing the subgraphs for each variable (x, !x) and for each clause (a triable). But I am not getting,how to do other way round?
I was thinking of first forming a DNF ,with electing k vertices at first and then convert it to a CNF, by enumerating all clauses. Is there any other method?