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==Remarks==
A planar graph is dual-critical if and only if its dual is factor-critical. It is not difficult to prove that if a graph is dual-critical, then its building procedure can be started with any of its nodes. There is a randomized algorithm based on computing the rank of a matrix with indeterminates<ref>B. Szegedy, Ch. Szegedy, Symplectic spaces and ear decompositions of matroids, Combinatorica 26(3): 353-377 (2006) [http://dx.doi.org/10.1007/s00493-006-0020-3 DOI link]</ref>.
The class of dual-critical graphs is somewhat unique from the point of view of constructive characterizations: it is defined via a constructive characterization, nevertheless, the complexity of membership testing is open.
==References==
