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
Recommended Citation
Oxley, J., & Singh, J. (2022). THE SMALLEST CLASSES OF BINARY AND TERNARY MATROIDS CLOSED UNDER DIRECT SUMS AND COMPLEMENTS. SIAM Journal on Discrete Mathematics, 36 (3), 2051-2072. https://doi.org/10.1137/21M1453852