Bicircular Matroids Representable over GF(4) or GF(5)

Deborah Chun; Tyler Moss; Dan Slilaty; Xiangqian Zhou

doi:10.1016/j.disc.2016.03.017

Bicircular Matroids Representable over GF(4) or GF(5)

Deborah Chun, Tyler Moss, Dan Slilaty, Xiangqian Zhou

Mathematics and Statistics

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

Abstract

Given a bicircular matroid B(G) and q∈{4,5}, we characterize when the bicircular matroid B(G) is GF(q)-representable by precisely describing the structure of G. These descriptions yield polynomial-time algorithms with input G to certify if B(G) is or is not GF(q)-representable.

Original language	American English
Journal	Discrete Mathematics
Volume	339
DOIs	https://doi.org/10.1016/j.disc.2016.03.017
State	Published - Sep 6 2016

Keywords

Bicircular Matroid
Frame Matroid
Frame Matrix
Gain Graph
Antivoltage

Disciplines

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

Access to Document

10.1016/j.disc.2016.03.017License: CC BY

Cite this

@article{009ed5f42db847ac885e3c6c77199f14,

title = "Bicircular Matroids Representable over GF(4) or GF(5)",

abstract = " Given a bicircular matroid B(G) and q∈{4,5}, we characterize when the bicircular matroid B(G) is GF(q)-representable by precisely describing the structure of G. These descriptions yield polynomial-time algorithms with input G to certify if B(G) is or is not GF(q)-representable.",

keywords = "Bicircular Matroid, Frame Matroid, Frame Matrix, Gain Graph, Antivoltage",

author = "Deborah Chun and Tyler Moss and Dan Slilaty and Xiangqian Zhou",

year = "2016",

month = sep,

day = "6",

doi = "10.1016/j.disc.2016.03.017",

language = "American English",

volume = "339",

journal = "Discrete Mathematics",

}

TY - JOUR

T1 - Bicircular Matroids Representable over GF(4) or GF(5)

AU - Chun, Deborah

AU - Moss, Tyler

AU - Slilaty, Dan

AU - Zhou, Xiangqian

PY - 2016/9/6

Y1 - 2016/9/6

N2 - Given a bicircular matroid B(G) and q∈{4,5}, we characterize when the bicircular matroid B(G) is GF(q)-representable by precisely describing the structure of G. These descriptions yield polynomial-time algorithms with input G to certify if B(G) is or is not GF(q)-representable.

AB - Given a bicircular matroid B(G) and q∈{4,5}, we characterize when the bicircular matroid B(G) is GF(q)-representable by precisely describing the structure of G. These descriptions yield polynomial-time algorithms with input G to certify if B(G) is or is not GF(q)-representable.

KW - Bicircular Matroid

KW - Frame Matroid

KW - Frame Matrix

KW - Gain Graph

KW - Antivoltage

UR - https://corescholar.libraries.wright.edu/math/304

U2 - 10.1016/j.disc.2016.03.017

DO - 10.1016/j.disc.2016.03.017

M3 - Article

VL - 339

JO - Discrete Mathematics

JF - Discrete Mathematics

ER -

Bicircular Matroids Representable over GF(4) or GF(5)

Abstract

Keywords

Disciplines

Access to Document

Other files and links

Cite this