{"id":"https://openalex.org/W2974909663","doi":"https://doi.org/10.37236/9039","title":"Monochromatic Components in Edge-Coloured Graphs with Large Minimum Degree","display_name":"Monochromatic Components in Edge-Coloured Graphs with Large Minimum Degree","publication_year":2021,"publication_date":"2021-01-14","ids":{"openalex":"https://openalex.org/W2974909663","doi":"https://doi.org/10.37236/9039","mag":"2974909663"},"language":"en","primary_location":{"id":"doi:10.37236/9039","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9039","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p10/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p10/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000751387","display_name":"Hannah Guggiari","orcid":"https://orcid.org/0000-0002-0525-0039"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Hannah Guggiari","raw_affiliation_strings":["University of Oxford"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045091550","display_name":"Alex Scott","orcid":"https://orcid.org/0000-0003-4489-5988"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alex Scott","raw_affiliation_strings":["University of Oxford"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":0.6185,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.53674328,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"28","issue":"1","first_page":null,"last_page":null},"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":0.9983000159263611,"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":0.9983000159263611,"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":0.9914000034332275,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9825000166893005,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/monochromatic-color","display_name":"Monochromatic color","score":0.8701009750366211},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8574185371398926},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7677895426750183},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7001235485076904},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6797374486923218},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5156487226486206},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.45406574010849},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.41692161560058594},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3280932605266571},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.26210764050483704},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.06955227255821228},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06360617280006409}],"concepts":[{"id":"https://openalex.org/C40833965","wikidata":"https://www.wikidata.org/wiki/Q6901438","display_name":"Monochromatic color","level":2,"score":0.8701009750366211},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8574185371398926},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7677895426750183},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7001235485076904},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6797374486923218},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5156487226486206},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.45406574010849},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.41692161560058594},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3280932605266571},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26210764050483704},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.06955227255821228},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06360617280006409},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/9039","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9039","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p10/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1909.09178","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.09178","pdf_url":"https://arxiv.org/pdf/1909.09178","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":"mag:2974909663","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1909.09178","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1909.09178","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1909.09178","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.37236/9039","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9039","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p10/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320319993","display_name":"Leverhulme Trust","ror":"https://ror.org/012mzw131"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2974909663.pdf","grobid_xml":"https://content.openalex.org/works/W2974909663.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W78420916","https://openalex.org/W1967323669","https://openalex.org/W2752166164","https://openalex.org/W2808095783","https://openalex.org/W3017992347","https://openalex.org/W3035042746"],"related_works":["https://openalex.org/W2752166164","https://openalex.org/W3067323280","https://openalex.org/W2808095783","https://openalex.org/W2944181870","https://openalex.org/W3046202471","https://openalex.org/W2218388935","https://openalex.org/W2952200477","https://openalex.org/W2977085300","https://openalex.org/W2913964323","https://openalex.org/W2115705527","https://openalex.org/W2993218614","https://openalex.org/W3103628474","https://openalex.org/W2133376124","https://openalex.org/W2951648952","https://openalex.org/W2904662490","https://openalex.org/W2963207566","https://openalex.org/W2047807138","https://openalex.org/W1701283134","https://openalex.org/W2775561983","https://openalex.org/W2981171106"],"abstract_inverted_index":{"For":[0,28],"every":[1,9],"$n\\in\\mathbb{N}$":[2],"and":[3,70],"$k\\geqslant2$,":[4],"it":[5,30],"is":[6,31,62],"known":[7,32],"that":[8,33,55],"$k$-edge-colouring":[10],"of":[11,23,60,68],"the":[12,34,56],"complete":[13,35],"graph":[14,36,42],"on":[15],"$n$":[16],"vertices":[17],"contains":[18],"a":[19,41,66],"monochromatic":[20],"connected":[21],"component":[22],"order":[24],"at":[25],"least":[26],"$\\frac{n}{k-1}$.":[27],"$k\\geqslant3$,":[29],"can":[37],"be":[38],"replaced":[39],"by":[40],"$G$":[43],"with":[44],"$\\delta(G)\\geqslant(1-\\varepsilon_k)n$":[45],"for":[46],"some":[47],"constant":[48],"$\\varepsilon_k$.":[49],"In":[50],"this":[51],"paper,":[52],"we":[53],"show":[54],"maximum":[57],"possible":[58],"value":[59],"$\\varepsilon_3$":[61],"$\\frac16$.":[63],"This":[64],"disproves":[65],"conjecture":[67],"Gy\u00e1rfas":[69],"S\u00e1rk\u00f6zy.":[71]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}
