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Combinatorica 17, pp 315-337 (1997). [http://dx.doi.org/10.1007/BF01215915 DOI link]</ref> studied the rank of the submatrices of the Tutte matrix.
This lead them to the formulation of the [[even factor problem]] and its solution via a random algorithm. Later, Gy. Pap and Szegő<ref>Gy. Pap, L. Szegő, On the maximum even factor in weakly symmetric graphs, Journal of Combinatorial Theory Ser. B, 91/2 (2004) 201-213, [http://dx.doi.org/10.1016/j.jctb.2004.01.001 DOI link] [http://www.cs.cornell.edu/%7Epap/evenfactor.pdf PDF]</ref> gave a min-max formula on the maximum cardinality of an even
factor; in a subsequent paper, Gy. Pap<ref>Gy. Pap, A Combinatorial Algorithm to Find a Maximum Even Factor, Lecture Notes in Computer Science, LNCS 3509, Springer Verlag (2005), 66-80. [http://dx.doi.org/10.1007/11496915_6 DOI link]</ref> also developed a purely combinatorial algorithm for finding an optimal solution. Iwata and Geelen<ref>J. Geelen, S. Iwata, Matroid matching via mixed skew-symmetric matrices,Combinatorica 25, pp 187-215 (2005) [http://dx.doi.org/10.1007/s00493-005-0013-7 DOI link] [http://www.math.uwaterloo.ca/~jfgeelen/publications/iwata.ps PDF]</ref> studied the rank of "T+K" where "T" is the Tutte matrix of a graph, and "K" is a [[wikipedia:skew symmetric matrix|skew symmetric matrix]]
One might be interested not only in deciding whether a polynomial matix is nonsingular, but also in (deterministically) finding
an evaluation with nonzero determinant, if there exists such. (The Schwartz-Zippel lemma
shows that there are indeed a very few evaluations with zero determinant for a nonsingular matrix). For the Tutte-matrix, Geelen<ref>J. Geelen, An algebraic matching algorithm,
Combinatorica 20, pp 61-70 (2000) [http://dx.doi.org/10.1007/s004930070031 DOI link] [http://www.math.uwaterloo.ca/~jfgeelen/publications/match.ps PS]</ref> gave a deterministic polynomial-time algorithm.
