Minimal non-orientable matroids of rank three

Hidefumi Hiraishi, Sonoko Moriyama

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 r with m elements. In this paper, we give an answer to the question in rank 3 that for every m≥. 7, there exists a minimal non-orientable matroid of rank 3 with m 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.

Original languageEnglish
Pages (from-to)123-137
Number of pages15
JournalEuropean Journal of Combinatorics
Volume50
DOIs
Publication statusPublished - 2015 Nov 1

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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