{"id":"https://openalex.org/W2013272583","doi":"https://doi.org/10.1112/jlms/jdu063","title":"Logarithmically small minors and topological minors","display_name":"Logarithmically small minors and topological minors","publication_year":2014,"publication_date":"2014-11-05","ids":{"openalex":"https://openalex.org/W2013272583","doi":"https://doi.org/10.1112/jlms/jdu063","mag":"2013272583"},"language":"en","primary_location":{"id":"doi:10.1112/jlms/jdu063","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdu063","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1309.7886","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Richard Montgomery","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Richard Montgomery","raw_affiliation_strings":["Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, Cambridgeshire, CB3 0WB, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, Cambridgeshire, CB3 0WB, United Kingdom","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":2.0572,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.83767471,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"91","issue":"1","first_page":"71","last_page":"88"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.7056999802589417,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.7056999802589417,"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":0.2240000069141388,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.016200000420212746,"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/degree","display_name":"Degree (music)","score":0.6593000292778015},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6140999794006348},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5292999744415283},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4812000095844269},{"id":"https://openalex.org/keywords/minor","display_name":"Minor (academic)","score":0.362199991941452},{"id":"https://openalex.org/keywords/simple-graph","display_name":"Simple graph","score":0.2696000039577484}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8679999709129333},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7358999848365784},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6593000292778015},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6140999794006348},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5292999744415283},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4812000095844269},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4512999951839447},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.362199991941452},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.2696000039577484},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.2615000009536743},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.25920000672340393},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.25600001215934753},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.25429999828338623}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1112/jlms/jdu063","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdu063","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1309.7886","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1309.7886","pdf_url":"https://arxiv.org/pdf/1309.7886","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/5611e65f-3b2d-455b-9030-4bffdfc2f836","is_oa":true,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/5611e65f-3b2d-455b-9030-4bffdfc2f836","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Montgomery, R 2015, 'Logarithmically-small minors and topological minors', Journal of the London Mathematical Society, vol. 91, no. 1, pp. 71-88. https://doi.org/10.1112/jlms/jdu063","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1309.7886","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1309.7886","pdf_url":"https://arxiv.org/pdf/1309.7886","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1966571632","https://openalex.org/W1967546560","https://openalex.org/W1976760940","https://openalex.org/W1989340449","https://openalex.org/W2017119382","https://openalex.org/W2019067855","https://openalex.org/W2047993669","https://openalex.org/W2067016370","https://openalex.org/W2071321409","https://openalex.org/W2076639460","https://openalex.org/W2084389562","https://openalex.org/W2109542562","https://openalex.org/W2122404357","https://openalex.org/W2151438396","https://openalex.org/W2170758948","https://openalex.org/W4250021881","https://openalex.org/W6642922641"],"related_works":[],"abstract_inverted_index":{"For":[0],"every":[1,95],"integer":[2,96],"t":[3,13,26,32,67,75,85,97,107,120,126,149,154,165,191,197,207,213,224],",":[4,84,98,164,206,223],"there":[5,99],"is":[6,100],"a":[7,30,73,101,124,152,195,211],"smallest":[8,102],"real":[9,103],"number":[10,104],"c":[11,24,65,189],"(":[12,25,66,82,106,119,142,148,162,184,190,204,221],")":[14,27,68,86,108,121,146,150,166,188,192,208,225],"such":[15,109],"that":[16,54,93,110],"any":[17,55,111],"graph":[18,56,112],"with":[19,57,113,137,179],"average":[20,61,114,138,180],"degree":[21,62,115,139,181],"at":[22,63,79,140,159,182,201,218],"least":[23,64,141,183],"must":[28,71,122],"contain":[29,72,123,151,193],"K":[31,74,125,153,196,212],"-minor":[33,76,198],"(proved":[34],"by":[35],"Mader).":[36],"Improving":[37],"on":[38],"results":[39],"of":[40,48,78,158,200,217],"Shapira":[41],"and":[42,52,60],"Sudakov,":[43],"we":[44,171],"prove":[45,130],"the":[46],"conjecture":[47],"Fiorini,":[49],"Joret,":[50],"Theis":[51],"Wood":[53],"n":[58,88,168,227],"vertices":[59,209],"+":[69,144,186],"\u03b5":[70,83,145,163,187,205,222],"consisting":[77,157,199,216],"most":[80,160,202,219],"C":[81,161,203,220],"log":[87,167,226],"vertices.":[89,169,228],"Mader":[90],"also":[91],"proved":[92],"for":[94,132,174],"s":[105,118,147],"larger":[116],"than":[117],"-topological":[127,155,214],"minor.":[128],"We":[129],"that,":[131,173],"sufficiently":[133,175],"large":[134,176],"t,":[135,177],"graphs":[136,178],"1":[143,185],"minor":[156,215],"Finally,":[170],"show":[172],"either":[194],"or":[210]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2016-06-24T00:00:00"}
