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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

Hidefumi HIRAISHI

The University of Tokyo

Sonoko MORIYAMA

Nihon University

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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

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@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},}

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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 -