If the set of vertices V has 2n elements then the Tutte matrix is a 2n × 2n 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 is not the Tutte polynomial of G.)
- R. Motwani, P. Raghavan (1995). Randomized Algorithms. Cambridge University Press.
- Allen B. Tucker (2004). Computer Science Handbook. CRC Press. ISBN 158488360X.
- W.T. Tutte (April 1947). "The factorization of linear graphs.". J. London Math. Soc. 22: 107-111. DOI:10.1112/jlms/s1-22.2.107. Retrieved on 2008-06-15. Research Blogging.