THE SMALLEST CLASSES OF BINARY AND TERNARY MATROIDS CLOSED UNDER DIRECT SUMS AND COMPLEMENTS

Document Type

Article

Publication Date

1-1-2022

Abstract

The class of cographs or complement-reducible graphs is the class of graphs that can be generated from K1 using the operations of disjoint union and complementation. By analogy, this paper introduces the class of binary comatroids as the class of matroids that can be generated from the empty matroid using the operations of direct sum and taking complements inside of binary projective space. We show that a proper flat of a binary comatroid is a binary comatroid. Our main result identifies those binary noncomatroids for which every proper flat is a binary comatroid. The paper also proves the corresponding results for ternary matroids.

Publication Source (Journal or Book title)

SIAM Journal on Discrete Mathematics

First Page

2051

Last Page

2072

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