Edmonds matrix

From Wikipedia, the free encyclopedia

In graph theory, the Edmonds matrix A of a bipartite graph G(U,V,E) with sets of vertices U = \{u_1, u_2, \dots , u_n \} and V = \{v_1, v_2, \dots , v_n\} is defined by

 A_{ij} = \left\{ \begin{array}{ll}
   x_{ij} & (u_i, v_j) \in E \\
   0 & (u_i, v_j) \notin E. 
 \end{array}\right.

where the xij are indeterminates. One application of the Edmonds matrix of a bipartite graph is that the graph admits a perfect matching if and only if the polynomial det(Aij) in the xij is not identically zero.

[edit] References

This combinatorics-related article is a stub. You can help Wikipedia by expanding it.