Colored matroid

In mathematics, a colored matroid is a matroid whose elements are labeled from a set of colors, which can be any set that suits the purpose, for instance the set of the first n positive integers, or the sign set {+, −}.

The interest in colored matroids is through their invariants, especially the colored Tutte polynomial,^[1] which generalizes the Tutte polynomial of a signed graph of Kauffman (1989).^[2]

There has also been study of optimization problems on matroids where the objective function of the optimization depends on the set of colors chosen as part of a matroid basis.^[3]

See also

• Bipartite matroid
• Rota's basis conjecture