The Highly Connected Matroids in Minor-Closed Classes

For any minor-closed class of matroids over a fixed finite field, we state an exact structural characterization for the sufficiently connected matroids in the class. We also state a number of conjectures that might be approachable using the structural characterization.

Saved in:
Bibliographic Details
Published in:Annals of combinatorics 2015-03, Vol.19 (1), p.107-123
Main Authors: Geelen, Jim, Gerards, Bert, Whittle, Geoff
Format: Article
Language:English
Subjects:
Combinatorics
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c358t-5762b7821159cd6eb81e6904e7725d462449663714a13d4e1da4037596c821ee3
cites cdi_FETCH-LOGICAL-c358t-5762b7821159cd6eb81e6904e7725d462449663714a13d4e1da4037596c821ee3
container_end_page 123
container_issue 1
container_start_page 107
container_title Annals of combinatorics
container_volume 19
creator Geelen, Jim
Gerards, Bert
Whittle, Geoff
description For any minor-closed class of matroids over a fixed finite field, we state an exact structural characterization for the sufficiently connected matroids in the class. We also state a number of conjectures that might be approachable using the structural characterization.
doi_str_mv 10.1007/s00026-015-0251-3
format article
fullrecord <record><control><sourceid>crossref_sprin</sourceid><recordid>TN_cdi_crossref_primary_10_1007_s00026_015_0251_3</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1007_s00026_015_0251_3</sourcerecordid><originalsourceid>FETCH-LOGICAL-c358t-5762b7821159cd6eb81e6904e7725d462449663714a13d4e1da4037596c821ee3</originalsourceid><addsrcrecordid>eNp9j8tOwzAQRS0EEqXwAezyA4YZP-MlioAitWJT1pYbT9tUIUF2WPTvcSlrVnOluWc0h7F7hAcEsI8ZAIThgJqD0MjlBZuBQMclOHX5m2teOuaa3eR8KMmCFDOm13uqFt1u3x-rZhwGaieK1SpMaexirrqhWnXDmHjTj7ksmj7kTPmWXW1Dn-nub87Zx8vzulnw5fvrW_O05K3U9cS1NWJja4GoXRsNbWok40CRtUJHZYRSzhhpUQWUURHGoEBa7UxbICI5Z3i-26Yx50Rb_5W6z5COHsGfvP3Z2xdvf_L2sjDizOTSHXaU_GH8TkN58x_oBwHVWBo</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>The Highly Connected Matroids in Minor-Closed Classes</title><source>Springer Link</source><creator>Geelen, Jim ; Gerards, Bert ; Whittle, Geoff</creator><creatorcontrib>Geelen, Jim ; Gerards, Bert ; Whittle, Geoff</creatorcontrib><description>For any minor-closed class of matroids over a fixed finite field, we state an exact structural characterization for the sufficiently connected matroids in the class. We also state a number of conjectures that might be approachable using the structural characterization.</description><identifier>ISSN: 0218-0006</identifier><identifier>EISSN: 0219-3094</identifier><identifier>DOI: 10.1007/s00026-015-0251-3</identifier><language>eng</language><publisher>Basel: Springer Basel</publisher><subject>Combinatorics ; Mathematics ; Mathematics and Statistics</subject><ispartof>Annals of combinatorics, 2015-03, Vol.19 (1), p.107-123</ispartof><rights>Springer Basel 2015</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c358t-5762b7821159cd6eb81e6904e7725d462449663714a13d4e1da4037596c821ee3</citedby><cites>FETCH-LOGICAL-c358t-5762b7821159cd6eb81e6904e7725d462449663714a13d4e1da4037596c821ee3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27900,27901</link.rule.ids></links><search><creatorcontrib>Geelen, Jim</creatorcontrib><creatorcontrib>Gerards, Bert</creatorcontrib><creatorcontrib>Whittle, Geoff</creatorcontrib><title>The Highly Connected Matroids in Minor-Closed Classes</title><title>Annals of combinatorics</title><addtitle>Ann. Comb</addtitle><description>For any minor-closed class of matroids over a fixed finite field, we state an exact structural characterization for the sufficiently connected matroids in the class. We also state a number of conjectures that might be approachable using the structural characterization.</description><subject>Combinatorics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0218-0006</issn><issn>0219-3094</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp9j8tOwzAQRS0EEqXwAezyA4YZP-MlioAitWJT1pYbT9tUIUF2WPTvcSlrVnOluWc0h7F7hAcEsI8ZAIThgJqD0MjlBZuBQMclOHX5m2teOuaa3eR8KMmCFDOm13uqFt1u3x-rZhwGaieK1SpMaexirrqhWnXDmHjTj7ksmj7kTPmWXW1Dn-nub87Zx8vzulnw5fvrW_O05K3U9cS1NWJja4GoXRsNbWok40CRtUJHZYRSzhhpUQWUURHGoEBa7UxbICI5Z3i-26Yx50Rb_5W6z5COHsGfvP3Z2xdvf_L2sjDizOTSHXaU_GH8TkN58x_oBwHVWBo</recordid><startdate>20150301</startdate><enddate>20150301</enddate><creator>Geelen, Jim</creator><creator>Gerards, Bert</creator><creator>Whittle, Geoff</creator><general>Springer Basel</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20150301</creationdate><title>The Highly Connected Matroids in Minor-Closed Classes</title><author>Geelen, Jim ; Gerards, Bert ; Whittle, Geoff</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c358t-5762b7821159cd6eb81e6904e7725d462449663714a13d4e1da4037596c821ee3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Combinatorics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Geelen, Jim</creatorcontrib><creatorcontrib>Gerards, Bert</creatorcontrib><creatorcontrib>Whittle, Geoff</creatorcontrib><collection>CrossRef</collection><jtitle>Annals of combinatorics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Geelen, Jim</au><au>Gerards, Bert</au><au>Whittle, Geoff</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Highly Connected Matroids in Minor-Closed Classes</atitle><jtitle>Annals of combinatorics</jtitle><stitle>Ann. Comb</stitle><date>2015-03-01</date><risdate>2015</risdate><volume>19</volume><issue>1</issue><spage>107</spage><epage>123</epage><pages>107-123</pages><issn>0218-0006</issn><eissn>0219-3094</eissn><abstract>For any minor-closed class of matroids over a fixed finite field, we state an exact structural characterization for the sufficiently connected matroids in the class. We also state a number of conjectures that might be approachable using the structural characterization.</abstract><cop>Basel</cop><pub>Springer Basel</pub><doi>10.1007/s00026-015-0251-3</doi><tpages>17</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0218-0006
ispartof Annals of combinatorics, 2015-03, Vol.19 (1), p.107-123
issn 0218-0006
0219-3094
language eng
recordid cdi_crossref_primary_10_1007_s00026_015_0251_3
source Springer Link
subjects Combinatorics
Mathematics
Mathematics and Statistics
title The Highly Connected Matroids in Minor-Closed Classes
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-24T09%3A56%3A06IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-crossref_sprin&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20Highly%20Connected%20Matroids%20in%20Minor-Closed%20Classes&rft.jtitle=Annals%20of%20combinatorics&rft.au=Geelen,%20Jim&rft.date=2015-03-01&rft.volume=19&rft.issue=1&rft.spage=107&rft.epage=123&rft.pages=107-123&rft.issn=0218-0006&rft.eissn=0219-3094&rft_id=info:doi/10.1007/s00026-015-0251-3&rft_dat=%3Ccrossref_sprin%3E10_1007_s00026_015_0251_3%3C/crossref_sprin%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c358t-5762b7821159cd6eb81e6904e7725d462449663714a13d4e1da4037596c821ee3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true