{"id":"https://openalex.org/W3167824428","doi":"https://doi.org/10.1017/s0963548321000201","title":"Monochromatic paths and cycles in 2-edge-coloured graphs with large minimum degree","display_name":"Monochromatic paths and cycles in 2-edge-coloured graphs with large minimum degree","publication_year":2021,"publication_date":"2021-06-14","ids":{"openalex":"https://openalex.org/W3167824428","doi":"https://doi.org/10.1017/s0963548321000201","mag":"3167824428"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548321000201","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548321000201","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/A5108264183","display_name":"J\u00f3zsef Balogh","orcid":null},"institutions":[{"id":"https://openalex.org/I153845743","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322","country_code":"RU","type":"education","lineage":["https://openalex.org/I153845743"]},{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["RU","US"],"is_corresponding":false,"raw_author_name":"J\u00f3zsef Balogh","raw_affiliation_strings":["Department of Mathematics, University of Illinois, Urbana\u2013Champaign, IL61801, USA","Moscow Institute of Physics and Technology, Dolgoprudny, Russian Federation"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Illinois, Urbana\u2013Champaign, IL61801, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Moscow Institute of Physics and Technology, Dolgoprudny, Russian Federation","institution_ids":["https://openalex.org/I153845743"]}]},{"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/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"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","US"],"is_corresponding":false,"raw_author_name":"Alexandr Kostochka","raw_affiliation_strings":["Department of Mathematics, University of Illinois, Urbana\u2013Champaign, IL61801, USA","Sobolev Institute of Mathematics, Novosibirsk630090, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Illinois, Urbana\u2013Champaign, IL61801, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk630090, Russia","institution_ids":["https://openalex.org/I4210096862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113493996","display_name":"M. I. Lavrov","orcid":null},"institutions":[{"id":"https://openalex.org/I172980758","display_name":"Kennesaw State University","ror":"https://ror.org/00jeqjx33","country_code":"US","type":"education","lineage":["https://openalex.org/I172980758"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mikhail Lavrov","raw_affiliation_strings":["Department of Mathematics, Kennesaw State University, Marietta, GA30060, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Kennesaw State University, Marietta, GA30060, USA","institution_ids":["https://openalex.org/I172980758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037977519","display_name":"Xujun Liu","orcid":"https://orcid.org/0000-0001-8995-959X"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Xujun Liu","raw_affiliation_strings":["Coordinated Science Laboratory, University of Illinois, Urbana\u2013Champaign, IL61801, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Coordinated Science Laboratory, University of Illinois, Urbana\u2013Champaign, IL61801, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5037977519"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":1.8614,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.83090379,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":97},"biblio":{"volume":"31","issue":"1","first_page":"109","last_page":"122"},"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":0.9991999864578247,"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"}},"topics":[{"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":0.9815999865531921,"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/combinatorics","display_name":"Combinatorics","score":0.8753596544265747},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7325363159179688},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.658661961555481},{"id":"https://openalex.org/keywords/monochromatic-color","display_name":"Monochromatic color","score":0.627010703086853},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5975370407104492},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5701693892478943},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4938269555568695},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3842521607875824},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15976032614707947}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8753596544265747},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7325363159179688},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.658661961555481},{"id":"https://openalex.org/C40833965","wikidata":"https://www.wikidata.org/wiki/Q6901438","display_name":"Monochromatic color","level":2,"score":0.627010703086853},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5975370407104492},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5701693892478943},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4938269555568695},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3842521607875824},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15976032614707947},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s0963548321000201","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548321000201","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:digitalcommons.kennesaw.edu:facpubs-6477","is_oa":false,"landing_page_url":"https://digitalcommons.kennesaw.edu/facpubs/5321","pdf_url":null,"source":{"id":"https://openalex.org/S4377196456","display_name":"DigitalCommons - Kennesaw State University (Kennesaw State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172980758","host_organization_name":"Kennesaw State University","host_organization_lineage":["https://openalex.org/I172980758"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Articles","raw_type":"text"},{"id":"pmh:oai:digitalcommons.kennesaw.edu:facpubs-6487","is_oa":false,"landing_page_url":"https://digitalcommons.kennesaw.edu/facpubs/5331","pdf_url":null,"source":{"id":"https://openalex.org/S4377196456","display_name":"DigitalCommons - Kennesaw State University (Kennesaw State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172980758","host_organization_name":"Kennesaw State University","host_organization_lineage":["https://openalex.org/I172980758"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W194635066","https://openalex.org/W1530753374","https://openalex.org/W1967323669","https://openalex.org/W1972826452","https://openalex.org/W1987996179","https://openalex.org/W1996876916","https://openalex.org/W2000934872","https://openalex.org/W2031273169","https://openalex.org/W2036204729","https://openalex.org/W2054235532","https://openalex.org/W2054249991","https://openalex.org/W2083584217","https://openalex.org/W2086491695","https://openalex.org/W2090747987","https://openalex.org/W2098682008","https://openalex.org/W2165941143","https://openalex.org/W2275005719","https://openalex.org/W2441619326","https://openalex.org/W3007721824","https://openalex.org/W4213289662","https://openalex.org/W4250210862","https://openalex.org/W6607843129"],"related_works":["https://openalex.org/W2509614667","https://openalex.org/W2963293152","https://openalex.org/W4302199713","https://openalex.org/W4282026465","https://openalex.org/W2626027010","https://openalex.org/W2963562790","https://openalex.org/W2909469610","https://openalex.org/W2755006503","https://openalex.org/W2988746064","https://openalex.org/W2045621845"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"graph":[2,6,30,35,86,174,217],"G":[3,13,81,97,175,218,228],"arrows":[4,32,45,182],"a":[5,16,33,231],"H":[7,20,36,46],"if":[8,27,72],"in":[9,53,60,135,224],"every":[10,39,67,94,104,120,166,171,214],"2-edge-colouring":[11,95,226],"of":[12,19,42,96,103,111,119,128,162,227,234],"there":[14,100,116,229],"exists":[15,230],"monochromatic":[17,232],"copy":[18],".":[21,239],"Schelp":[22,163],"had":[23],"the":[24,28,112,129,136,150,160,183,197],"idea":[25],"that":[26,65,138,164,206],"complete":[29],"$K_n$":[31,43],"small":[34],",":[37,47,71,91,98,170,223],"then":[38,92],"\u2018dense\u2019":[40],"subgraph":[41],"also":[44,158],"and":[48,80,149,204,213],"he":[49],"outlined":[50],"some":[51],"problems":[52],"this":[54,61],"direction.":[55],"Our":[56,131],"main":[57],"result":[58,132],"is":[59,82,133],"spirit.":[62],"We":[63],"prove":[64],"for":[66,93,165,193,207],"sufficiently":[68,167,194],"large":[69,168,195],"n":[70,84,169,188,196,215],"$n":[73],"=":[74],"3t+r$":[75],"where":[76,209],"$r":[77,210],"\\in":[78,211],"\\{0,1,2\\}$":[79,212],"an":[83],"-vertex":[85,173,216],"with":[87,176,186,219],"$\\delta(G)":[88,220],"\\ge":[89,221],"(3n-1)/4$":[90],"either":[99],"are":[101,117],"cycles":[102,118,141],"length":[105,122,143,235],"$\\{3,":[106],"4,":[107],"5,":[108],"\\dots,":[109,126],"2t+r\\}$":[110],"same":[113],"colour,":[114],"or":[115],"even":[121],"$\\{4,":[123],"6,":[124],"8,":[125],"2t+2\\}$":[127],"samecolour.":[130],"tight":[134],"sense":[137],"no":[139],"longer":[140],"(of":[142],"$>2t+r$":[144],")":[145],"can":[146],"be":[147,155],"guaranteed":[148],"minimum":[151,177],"degree":[152,178],"condition":[153],"cannot":[154],"reduced.":[156],"It":[157],"implies":[159,192],"conjecture":[161,198],"$(3t-1)$":[172],"larger":[179],"than":[180],"$3|V(G)|/4$":[181],"path":[184],"$P_{2n}$":[185],"2":[187],"vertices.":[189],"Moreover,":[190],"it":[191],"by":[199],"Benevides,":[200],"\u0141uczak,":[201],"Scott,":[202],"Skokan":[203],"White":[205],"$n=3t+r$":[208],"3n/4$":[222],"each":[225],"cycle":[233],"at":[236],"least":[237],"$2t+r$":[238]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}