Document Type
Article
Publication Date
5-1-2021
Abstract
In 2004, Ehrenfeucht, Harju, and Rozenberg showed that any graph on a vertex set V can be obtained from a complete graph on V via a sequence of the operations of complementation, switching edges and non-edges at a vertex, and local complementation. The last operation involves taking the complement in the neighbourhood of a vertex. In this paper, we consider natural generalizations of these operations for binary matroids and explore their behaviour. We characterize all binary matroids obtainable from the binary projective geometry of rank r under the operations of complementation and switching. Moreover, we show that not all binary matroids of rank at most r can be obtained from a projective geometry of rank r via a sequence of the three generalized operations. We introduce a fourth operation and show that, with this additional operation, we are able to obtain all binary matroids.
Publication Source (Journal or Book title)
Advances in Applied Mathematics
Recommended Citation
Oxley, J., & Singh, J. (2021). Complementation, local complementation, and switching in binary matroids. Advances in Applied Mathematics, 126 https://doi.org/10.1016/j.aam.2020.102041