On maximum-sized near-regular and 6√1-matroids
The classes of near-regular and 6√1-matroids arise in the study of matroids representable over GF(3) and other fields. For example, a matroid is representable over all fields except possibly GF(2) if and only if it is near-regular, and a matroid is representable over GF(3) and GF(4) if and only if it is a 6√1-matroid. This paper determines the max-imum sizes of a simple rank-r near-regular and a simple rank-r 6√1-matroid and determines all such matroids having these sizes. © Springer-Verlag 1998.
Publication Source (Journal or Book title)
Graphs and Combinatorics
Oxley, J., Vertigan, D., & Whittle, G. (1998). On maximum-sized near-regular and 6√1-matroids. Graphs and Combinatorics, 14 (2), 163-179. https://doi.org/10.1007/s003730050024