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. ^[1]

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Table of Contents

1. 6 relations: Bipartite matroid, Mathematics, Matroid, Rota's basis conjecture, Signed graph, Tutte polynomial.

Bipartite matroid

In mathematics, a bipartite matroid is a matroid all of whose circuits have even size. Colored matroid and bipartite matroid are matroid theory.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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Matroid

In combinatorics, a branch of mathematics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. Colored matroid and matroid are matroid theory.

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Rota's basis conjecture

In linear algebra and matroid theory, Rota's basis conjecture is an unproven conjecture concerning rearrangements of bases, named after Gian-Carlo Rota. Colored matroid and Rota's basis conjecture are matroid theory.

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Signed graph

In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. Colored matroid and signed graph are matroid theory.

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Tutte polynomial

The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a graph polynomial. Colored matroid and Tutte polynomial are matroid theory.

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References

[1] https://en.wikipedia.org/wiki/Colored_matroid

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