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It is known that finding a perfect matching in a general graph
is
-equivalent to finding a perfect matching
in a 3-regular ( cubic) graph.
In this paper we extend this result to both, planar and bipartite cases.
In particular we prove that the construction
problem for perfect matchings in planar graphs
is as difficult as in the case of planar cubic graphs
like it is known to be the case for the famous Map Four-Coloring problem.
Moreover we prove that the existence and construction...
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