If the set of vertices V has n elements then the Tutte matrix is an n × n matrix A with entries
where the xij are indeterminates. The determinant of this skew-symmetric matrix is then a polynomial (in the variables xij, i < j ): this coincides with the square of the pfaffian of the matrix A and is non-zero (as a polynomial) if and only if a perfect matching exists. (It should be noted that this polynomial is not the Tutte polynomial of G.)
- R. Motwani, P. Raghavan (1995). Randomized Algorithms. Cambridge University Press. p. 167.
- Allen B. Tucker (2004). Computer Science Handbook. CRC Press. p. 12.19. ISBN 1-58488-360-X.
- W.T. Tutte (April 1947). "The factorization of linear graphs" (PDF). J. London Math. Soc. 22 (2): 107–111. doi:10.1112/jlms/s1-22.2.107. Retrieved 2008-06-15.
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