Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4653246 | European Journal of Combinatorics | 2015 | 15 Pages |
Abstract
Minimal non-orientable matroids have been investigated as a threshold between orientability and non-orientability. The Fano matroid and the MacLane matroid are well-known minimal non-orientable matroids of rank 3. A natural question is whether there exists a minimal non-orientable matroid of every rank rr with mm elements. In this paper, we give an answer to the question in rank 3 that for every m≥7m≥7, there exists a minimal non-orientable matroid of rank 3 with mm elements. To prove this statement, we construct two new infinite families of minimal non-orientable matroids of rank 3. Furthermore we also investigate representability of the two infinite families.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Hidefumi Hiraishi, Sonoko Moriyama,