Biased graphs whose matroids are special binary matroids

Thomas Zaslavsky

doi:10.1007/BF01787483

Biased graphs whose matroids are special binary matroids

Thomas Zaslavsky

Mathematics and Statistics

Binghamton University

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

15 Scopus citations

Abstract

A biased graph is a graph together with a class of polygons such that no theta subgraph contains exactly two members of the class. To a biased graph Ω are naturally associated three edge matroids:G(Ω), L(Ω), L₀(Ω). We determine all biased graphs for which any of these matroids is isomorphic to the Fano plane, the polygon matroid of K₄, K₅ or K_3,3, any of their duals, Bixby's regular matroid R₁₀, or the polygon matroid of K_m for m > 5. In each case the bias is derived from edge signs. We conclude by finding the biased graphs Ω for which L₀(Ω) is not a graphic [or, regular matroid but every proper contraction is.

Original language	English
Pages (from-to)	77-93
Number of pages	17
Journal	Graphs and Combinatorics
Volume	6
Issue number	1
DOIs	https://doi.org/10.1007/BF01787483
State	Published - Mar 1990

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title = "Biased graphs whose matroids are special binary matroids",

abstract = "A biased graph is a graph together with a class of polygons such that no theta subgraph contains exactly two members of the class. To a biased graph Ω are naturally associated three edge matroids:G(Ω), L(Ω), L0(Ω). We determine all biased graphs for which any of these matroids is isomorphic to the Fano plane, the polygon matroid of K4, K5 or K3,3, any of their duals, Bixby's regular matroid R10, or the polygon matroid of Km for m > 5. In each case the bias is derived from edge signs. We conclude by finding the biased graphs Ω for which L0(Ω) is not a graphic [or, regular matroid but every proper contraction is.",

author = "Thomas Zaslavsky",

year = "1990",

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doi = "10.1007/BF01787483",

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N2 - A biased graph is a graph together with a class of polygons such that no theta subgraph contains exactly two members of the class. To a biased graph Ω are naturally associated three edge matroids:G(Ω), L(Ω), L0(Ω). We determine all biased graphs for which any of these matroids is isomorphic to the Fano plane, the polygon matroid of K4, K5 or K3,3, any of their duals, Bixby's regular matroid R10, or the polygon matroid of Km for m > 5. In each case the bias is derived from edge signs. We conclude by finding the biased graphs Ω for which L0(Ω) is not a graphic [or, regular matroid but every proper contraction is.

AB - A biased graph is a graph together with a class of polygons such that no theta subgraph contains exactly two members of the class. To a biased graph Ω are naturally associated three edge matroids:G(Ω), L(Ω), L0(Ω). We determine all biased graphs for which any of these matroids is isomorphic to the Fano plane, the polygon matroid of K4, K5 or K3,3, any of their duals, Bixby's regular matroid R10, or the polygon matroid of Km for m > 5. In each case the bias is derived from edge signs. We conclude by finding the biased graphs Ω for which L0(Ω) is not a graphic [or, regular matroid but every proper contraction is.

UR - https://www.scopus.com/pages/publications/0040266780

U2 - 10.1007/BF01787483

DO - 10.1007/BF01787483

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VL - 6

SP - 77

EP - 93

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

IS - 1

ER -

Biased graphs whose matroids are special binary matroids

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