IEICE TRANSACTIONS on Fundamentals
Excluded Minors of Rank 3 for Orientability and Representability
Summary :
We investigate excluded minor characterizations of two fundamental classes of matroids: orientable matroids and representable matroids. We prove (i) for any fixed field F, there exist infinitely many excluded minors of rank 3 for the union of the class of orientable matroids and the class of F-representable matroids, and (ii) for any fixed field F with characteristic 0, there exist infinitely many orientable excluded minors of rank 3 for intersection of the class of orientable matroids and the class of F-representable matroids. We show these statements by explicitly constructing infinite families of excluded minors.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E101-A No.9 pp.1355-1362
- Publication Date
- 2018/09/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E101.A.1355
- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
- Category
Authors
Hidefumi HIRAISHI
The University of Tokyo
Sonoko MORIYAMA
Nihon University
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
Hidefumi HIRAISHI, Sonoko MORIYAMA, "Excluded Minors of Rank 3 for Orientability and Representability" in IEICE TRANSACTIONS on Fundamentals,
vol. E101-A, no. 9, pp. 1355-1362, September 2018, doi: 10.1587/transfun.E101.A.1355.
Abstract: We investigate excluded minor characterizations of two fundamental classes of matroids: orientable matroids and representable matroids. We prove (i) for any fixed field F, there exist infinitely many excluded minors of rank 3 for the union of the class of orientable matroids and the class of F-representable matroids, and (ii) for any fixed field F with characteristic 0, there exist infinitely many orientable excluded minors of rank 3 for intersection of the class of orientable matroids and the class of F-representable matroids. We show these statements by explicitly constructing infinite families of excluded minors.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.1355/_p
Copy
@ARTICLE{e101-a_9_1355,
author={Hidefumi HIRAISHI, Sonoko MORIYAMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Excluded Minors of Rank 3 for Orientability and Representability},
year={2018},
volume={E101-A},
number={9},
pages={1355-1362},
abstract={We investigate excluded minor characterizations of two fundamental classes of matroids: orientable matroids and representable matroids. We prove (i) for any fixed field F, there exist infinitely many excluded minors of rank 3 for the union of the class of orientable matroids and the class of F-representable matroids, and (ii) for any fixed field F with characteristic 0, there exist infinitely many orientable excluded minors of rank 3 for intersection of the class of orientable matroids and the class of F-representable matroids. We show these statements by explicitly constructing infinite families of excluded minors.},
keywords={},
doi={10.1587/transfun.E101.A.1355},
ISSN={1745-1337},
month={September},}
Copy
TY - JOUR
TI - Excluded Minors of Rank 3 for Orientability and Representability
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1355
EP - 1362
AU - Hidefumi HIRAISHI
AU - Sonoko MORIYAMA
PY - 2018
DO - 10.1587/transfun.E101.A.1355
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E101-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2018
AB - We investigate excluded minor characterizations of two fundamental classes of matroids: orientable matroids and representable matroids. We prove (i) for any fixed field F, there exist infinitely many excluded minors of rank 3 for the union of the class of orientable matroids and the class of F-representable matroids, and (ii) for any fixed field F with characteristic 0, there exist infinitely many orientable excluded minors of rank 3 for intersection of the class of orientable matroids and the class of F-representable matroids. We show these statements by explicitly constructing infinite families of excluded minors.
ER -
English
