Unavoidable Minors of Large 4-Connected Bicircular Matroids

Deborah Chun; Tyler Moss; Dan Slilaty; Xiangqian Zhou

doi:10.1007/s00026-015-0256-y

Unavoidable Minors of Large 4-Connected Bicircular Matroids

Deborah Chun, Tyler Moss, Dan Slilaty, Xiangqian Zhou

Mathematics and Statistics

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Abstract

It is known that any 3-connected matroid that is large enough is certain to contain a minor of a given size belonging to one of a few special classes of matroids. This paper proves a similar unavoidable minor result for large 4-connected bicircular matroids. The main result follows from establishing the list of unavoidable minors of large 4-biconnected graphs, which are the graphs representing the 4-connected bicircular matroids. This paper also gives similar results for internally 4-connected and vertically 4-connected bicircular matroids.

Original language	American English
Journal	Annals of Combinatorics
Volume	19
DOIs	https://doi.org/10.1007/s00026-015-0256-y
State	Published - Jan 1 2015

Disciplines

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

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10.1007/s00026-015-0256-yLicense: CC BY

Unavoidable Minors of Large 4-Connected Bicircular MatroidsFinal published version, 198 KBLicense: CC BY

Cite this

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title = "Unavoidable Minors of Large 4-Connected Bicircular Matroids",

abstract = " It is known that any 3-connected matroid that is large enough is certain to contain a minor of a given size belonging to one of a few special classes of matroids. This paper proves a similar unavoidable minor result for large 4-connected bicircular matroids. The main result follows from establishing the list of unavoidable minors of large 4-biconnected graphs, which are the graphs representing the 4-connected bicircular matroids. This paper also gives similar results for internally 4-connected and vertically 4-connected bicircular matroids.",

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

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AU - Chun, Deborah

AU - Moss, Tyler

AU - Slilaty, Dan

AU - Zhou, Xiangqian

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Y1 - 2015/1/1

N2 - It is known that any 3-connected matroid that is large enough is certain to contain a minor of a given size belonging to one of a few special classes of matroids. This paper proves a similar unavoidable minor result for large 4-connected bicircular matroids. The main result follows from establishing the list of unavoidable minors of large 4-biconnected graphs, which are the graphs representing the 4-connected bicircular matroids. This paper also gives similar results for internally 4-connected and vertically 4-connected bicircular matroids.

AB - It is known that any 3-connected matroid that is large enough is certain to contain a minor of a given size belonging to one of a few special classes of matroids. This paper proves a similar unavoidable minor result for large 4-connected bicircular matroids. The main result follows from establishing the list of unavoidable minors of large 4-biconnected graphs, which are the graphs representing the 4-connected bicircular matroids. This paper also gives similar results for internally 4-connected and vertically 4-connected bicircular matroids.

UR - https://corescholar.libraries.wright.edu/math/313

U2 - 10.1007/s00026-015-0256-y

DO - 10.1007/s00026-015-0256-y

M3 - Article

VL - 19

JO - Annals of Combinatorics

JF - Annals of Combinatorics

ER -

Unavoidable Minors of Large 4-Connected Bicircular Matroids

Abstract

Disciplines

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