A note on nongraphic matroids

Takao Asano; Takao Nishizeki; P. D. Seymour

doi:10.1016/0095-8956(84)90062-5

A note on nongraphic matroids

Takao Asano, Takao Nishizeki, P. D. Seymour

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

Tutte found an excluded minor characterization of graphic matroids with five excluded minors. A variation on Tutte's result is presented here. Let {e, f, g} be a circuit of a 3-connected nongraphic matroid M. Then M has a minor using e, f, g isomorphic to either the 4-point line, the Fano matroid, or the bond matroid of K_3,3.

Original language	English (US)
Pages (from-to)	290-293
Number of pages	4
Journal	Journal of Combinatorial Theory, Series B
Volume	37
Issue number	3
DOIs	https://doi.org/10.1016/0095-8956(84)90062-5
State	Published - Dec 1984
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/0095-8956(84)90062-5

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title = "A note on nongraphic matroids",

abstract = "Tutte found an excluded minor characterization of graphic matroids with five excluded minors. A variation on Tutte's result is presented here. Let {e, f, g} be a circuit of a 3-connected nongraphic matroid M. Then M has a minor using e, f, g isomorphic to either the 4-point line, the Fano matroid, or the bond matroid of K3,3.",

author = "Takao Asano and Takao Nishizeki and Seymour, {P. D.}",

note = "Funding Information: * Research partially supported by NSF Grant MCS 8302266.",

year = "1984",

month = dec,

doi = "10.1016/0095-8956(84)90062-5",

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T1 - A note on nongraphic matroids

AU - Asano, Takao

AU - Nishizeki, Takao

AU - Seymour, P. D.

N1 - Funding Information: * Research partially supported by NSF Grant MCS 8302266.

PY - 1984/12

Y1 - 1984/12

N2 - Tutte found an excluded minor characterization of graphic matroids with five excluded minors. A variation on Tutte's result is presented here. Let {e, f, g} be a circuit of a 3-connected nongraphic matroid M. Then M has a minor using e, f, g isomorphic to either the 4-point line, the Fano matroid, or the bond matroid of K3,3.

AB - Tutte found an excluded minor characterization of graphic matroids with five excluded minors. A variation on Tutte's result is presented here. Let {e, f, g} be a circuit of a 3-connected nongraphic matroid M. Then M has a minor using e, f, g isomorphic to either the 4-point line, the Fano matroid, or the bond matroid of K3,3.

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U2 - 10.1016/0095-8956(84)90062-5

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AN - SCOPUS:0347466299

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JO - Journal of Combinatorial Theory, Series B

JF - Journal of Combinatorial Theory, Series B

IS - 3

ER -

A note on nongraphic matroids

Abstract

All Science Journal Classification (ASJC) codes

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