{"id":"https://openalex.org/W2024748609","doi":"https://doi.org/10.1017/s0963548311000174","title":"Minors in Graphs with High Chromatic Number","display_name":"Minors in Graphs with High Chromatic Number","publication_year":2011,"publication_date":"2011-04-13","ids":{"openalex":"https://openalex.org/W2024748609","doi":"https://doi.org/10.1017/s0963548311000174","mag":"2024748609"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548311000174","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548311000174","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001988513","display_name":"Thomas B\u00f6hme","orcid":null},"institutions":[{"id":"https://openalex.org/I119449181","display_name":"Technische Universit\u00e4t Ilmenau","ror":"https://ror.org/01weqhp73","country_code":"DE","type":"education","lineage":["https://openalex.org/I119449181"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"THOMAS B\u00d6HME","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Technische Universit\u00e4t Ilmenau, Ilmenau, Germany (e-mail:","Institut f\u00fcr mathematik, technische universit\u00e4t ilmenau, ilmenau, germany (e-mail: tboehme@theoinf.tu-ilmenau.de)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Ilmenau, Ilmenau, Germany (e-mail:","institution_ids":["https://openalex.org/I119449181"]},{"raw_affiliation_string":"Institut f\u00fcr mathematik, technische universit\u00e4t ilmenau, ilmenau, germany (e-mail: tboehme@theoinf.tu-ilmenau.de)#TAB#","institution_ids":["https://openalex.org/I119449181"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080894223","display_name":"Alexandr Kostochka","orcid":"https://orcid.org/0000-0002-6363-3804"},"institutions":[{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"ALEXANDR KOSTOCHKA","raw_affiliation_strings":["Department of Mathematics, University of Illinois, Urbana, IL 61801, USA and Sobolev Institute of Mathematics, Novosibirsk, Russia (e-mail:","Department of mathematics, university of illinois, urbana, il 61801, usa and sobolev institute of mathematics, novosibirsk, russia (e-mail: kostochk@math.uiuc.edu)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Illinois, Urbana, IL 61801, USA and Sobolev Institute of Mathematics, Novosibirsk, Russia (e-mail:","institution_ids":["https://openalex.org/I4210096862"]},{"raw_affiliation_string":"Department of mathematics, university of illinois, urbana, il 61801, usa and sobolev institute of mathematics, novosibirsk, russia (e-mail: kostochk@math.uiuc.edu)#TAB#","institution_ids":["https://openalex.org/I4210096862"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084708925","display_name":"Andrew Thomason","orcid":"https://orcid.org/0000-0002-1805-4221"},"institutions":[{"id":"https://openalex.org/I4210131390","display_name":"London Mathematical Laboratory","ror":"https://ror.org/03cznfh76","country_code":"GB","type":"facility","lineage":["https://openalex.org/I4210131390"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"ANDREW THOMASON","raw_affiliation_strings":["DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, UK (e-mail:","Dpmms, centre for mathematical sciences, wilberforce road, cambridge, uk (e-mail: a.g.thomason@dpmms.cam.ac.uk)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, UK (e-mail:","institution_ids":["https://openalex.org/I4210131390"]},{"raw_affiliation_string":"Dpmms, centre for mathematical sciences, wilberforce road, cambridge, uk (e-mail: a.g.thomason@dpmms.cam.ac.uk)#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.10553333,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"20","issue":"4","first_page":"513","last_page":"518"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.8637248277664185},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7686293721199036},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5510903596878052},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3733114004135132}],"concepts":[{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.8637248277664185},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7686293721199036},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5510903596878052},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3733114004135132}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0963548311000174","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548311000174","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.224.6507","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.224.6507","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uiuc.edu/%7Ekostochk/docs/2012/cpc11bs.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1033655406","https://openalex.org/W1520619927","https://openalex.org/W1988449255","https://openalex.org/W2052409046","https://openalex.org/W2071321409","https://openalex.org/W2095384119","https://openalex.org/W2164194022","https://openalex.org/W2799004609","https://openalex.org/W4241566937","https://openalex.org/W7057663353"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"We":[0],"develop":[1],"lower":[2],"bounds":[3],"on":[4],"the":[5],"Hadwiger":[6],"number":[7,28],"h":[8,31],"(":[9,32],"G":[10,14,22,33],")":[11,34],"of":[12],"graphs":[13],"with":[15],"high":[16],"chromatic":[17,27],"number.":[18],"In":[19],"particular,":[20],"if":[21],"has":[23],"n":[24,39],"vertices":[25],"and":[26],"k":[29,37],"then":[30],"\u2265":[35],"(4":[36],"\u2212":[38],")/3.":[40]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}