We present a new polynomial-time algorithm for finding minimal
vertex covers in graphs. The algorithm finds a minimum vertex cover
in all known examples of graphs. In view of the importance of the P
versus NP question, we ask if there exists a graph for which the
algorithm cannot find a minimum vertex cover. The algorithm is
demonstrated by finding minimum vertex covers for several famous
graphs, including two large benchmark graphs with hidden minimum
vertex covers. We implement the algorithm in C++ and provide a
demonstration program for Microsoft Windows.
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