TOPICS
Search

Binary Matroid

A binary matroid is a matroid representable by the columns of a matrix over the two-element finite field GF(2). A set of column labels is independent in the matroid precisely when the corresponding columns are linearly independent over GF(2).

Every graphic matroid is binary. For example, the columns of the incidence matrix of a loopless graph, interpreted over GF(2), represent its graphic matroid. Binary representability depends on the field, not merely on whether the entries of a representing matrix are 0 and 1.

See also

Circuit-Cocircuit Intersection Conjecture, Finite Field, Graphic Matroid, Matroid, Matroid Rank, White's Conjecture

Explore with Wolfram|Alpha

References

Oxley, J. G. Matroid Theory. Oxford, England: Oxford University Press, 1992.

Cite this as:

Weisstein, Eric W. "Binary Matroid." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BinaryMatroid.html

Subject classifications