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Strongly Base-Orderable Matroid

A strongly base-orderable matroid is a matroid such that, for any two matroid bases B_1 and B_2, there is a bijection phi:B_1->B_2 for which (B_1\X) union phi(X) is a matroid basis for every subset X subset= B_1 (Garami 2026).

Garami (2026) proved that two strongly base-orderable matroids, each admitting a matroid coloring with two colors, admit a common matroid coloring from every assignment of color lists of size 2.

See also

Matroid, Matroid Basis, Matroid Coloring

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References

Garami, B. "A Note on the List Chromatic Number of Two Matroids." 5 Oct 2026. https://arxiv.org/abs/2610.07318.

Cite this as:

Weisstein, Eric W. "Strongly Base-Orderable Matroid." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StronglyBase-OrderableMatroid.html

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