Properties

If a matroid is regular, so is its dual matroid, and so is every one of its minors. Every direct sum of regular matroids remains regular.

Every graphic matroid (and every co-graphic matroid) is regular. Conversely, every regular matroid may be constructed by combining graphic matroids, co-graphic matroids, and a certain ten-element matroid that is neither graphic nor co-graphic, using an operation

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