Clones in 3-Connected Frame Matroids

Jakayla Robbins; Dan Slilaty; Xiangqian Zhou

doi:10.1016/j.disc.2015.11.024

Clones in 3-Connected Frame Matroids

Jakayla Robbins, Dan Slilaty, Xiangqian Zhou

Mathematics and Statistics

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

Abstract

We determine the structure of clonal classes of 3-connected frame matroids in terms of the structure of biased graphs. Robbins has conjectured that a 3-connected non-uniform matroid with a clonal class of size q−1 is not GF(q) -representable. We confirm the conjecture for the class of frame matroids.

Original language	American English
Journal	Discrete Mathematics
Volume	339
DOIs	https://doi.org/10.1016/j.disc.2015.11.024
State	Published - Apr 6 2016

Keywords

Frame Matroids
Biased Graph
Clones
3-Connected

Disciplines

Applied Mathematics
Applied Statistics
Mathematics
Physical Sciences and Mathematics
Statistics and Probability

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10.1016/j.disc.2015.11.024License: CC BY

Cite this

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title = "Clones in 3-Connected Frame Matroids",

abstract = " We determine the structure of clonal classes of 3-connected frame matroids in terms of the structure of biased graphs. Robbins has conjectured that a 3-connected non-uniform matroid with a clonal class of size q−1 is not GF(q) -representable. We confirm the conjecture for the class of frame matroids.",

keywords = "Frame Matroids, Biased Graph, Clones, 3-Connected",

author = "Jakayla Robbins and Dan Slilaty and Xiangqian Zhou",

year = "2016",

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doi = "10.1016/j.disc.2015.11.024",

language = "American English",

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journal = "Discrete Mathematics",

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T1 - Clones in 3-Connected Frame Matroids

AU - Robbins, Jakayla

AU - Slilaty, Dan

AU - Zhou, Xiangqian

PY - 2016/4/6

Y1 - 2016/4/6

N2 - We determine the structure of clonal classes of 3-connected frame matroids in terms of the structure of biased graphs. Robbins has conjectured that a 3-connected non-uniform matroid with a clonal class of size q−1 is not GF(q) -representable. We confirm the conjecture for the class of frame matroids.

AB - We determine the structure of clonal classes of 3-connected frame matroids in terms of the structure of biased graphs. Robbins has conjectured that a 3-connected non-uniform matroid with a clonal class of size q−1 is not GF(q) -representable. We confirm the conjecture for the class of frame matroids.

KW - Frame Matroids

KW - Biased Graph

KW - Clones

KW - 3-Connected

UR - https://corescholar.libraries.wright.edu/math/300

U2 - 10.1016/j.disc.2015.11.024

DO - 10.1016/j.disc.2015.11.024

M3 - Article

VL - 339

JO - Discrete Mathematics

JF - Discrete Mathematics

ER -

Clones in 3-Connected Frame Matroids

Abstract

Keywords

Disciplines

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