{"id":"https://openalex.org/W7172402385","doi":"https://doi.org/10.48550/arxiv.2608.02522","title":"Locally bipartite subgraphs via multicolor Ramsey numbers","display_name":"Locally bipartite subgraphs via multicolor Ramsey numbers","publication_year":2026,"publication_date":"2026-08-03","ids":{"openalex":"https://openalex.org/W7172402385","doi":"https://doi.org/10.48550/arxiv.2608.02522"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.02522","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.02522","pdf_url":"https://arxiv.org/pdf/2608.02522","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,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.02522","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048260458","display_name":"Raphael Steiner","orcid":"https://orcid.org/0000-0002-4234-6136","observed_orcids":["https://orcid.org/0000-0002-4234-6136"]},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Steiner, Raphael","raw_affiliation_strings":["Department of Mathematics , ETH Z\u00fcrich , Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , ETH Z\u00fcrich , Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5048260458"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":1.0,"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":1.0,"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":0.0,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/erdos-hajnal-conjecture","display_name":"Erd\u0151s-Hajnal conjecture","score":0.9269999861717224},{"id":"https://openalex.org/keywords/multicolor-ramsey-numbers","display_name":"multicolor Ramsey numbers","score":0.8410000205039978},{"id":"https://openalex.org/keywords/odd-cycles","display_name":"odd cycles","score":0.8700000047683716},{"id":"https://openalex.org/keywords/iterated-logarithm","display_name":"iterated logarithm","score":0.7070000171661377},{"id":"https://openalex.org/keywords/fractional-chromatic-number","display_name":"fractional chromatic number","score":0.7850000262260437},{"id":"https://openalex.org/keywords/lovasz-theta-function","display_name":"Lov\u00e1sz theta function","score":0.9480000138282776}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8565999865531921},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8413000106811523},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7623999714851379},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6394000053405762},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5325999855995178},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5239999890327454},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4805000126361847},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41670000553131104},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.3939000070095062},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.3702999949455261},{"id":"https://openalex.org/C2777831296","wikidata":"https://www.wikidata.org/wiki/Q12518","display_name":"Tower","level":2,"score":0.34529998898506165},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.32989999651908875},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.2897000014781952},{"id":"https://openalex.org/C2777434295","wikidata":"https://www.wikidata.org/wiki/Q959831","display_name":"Girth (graph theory)","level":2,"score":0.289000004529953},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2847000062465668},{"id":"https://openalex.org/C125080357","wikidata":"https://www.wikidata.org/wiki/Q45715","display_name":"Complete graph","level":3,"score":0.2822999954223633},{"id":"https://openalex.org/C167750561","wikidata":"https://www.wikidata.org/wiki/Q1789512","display_name":"Critical graph","level":5,"score":0.27459999918937683},{"id":"https://openalex.org/C44115641","wikidata":"https://www.wikidata.org/wiki/Q918099","display_name":"Ramsey's theorem","level":3,"score":0.2720000147819519},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C2777478746","wikidata":"https://www.wikidata.org/wiki/Q5358910","display_name":"Elementary proof","level":2,"score":0.26080000400543213}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.02522","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.02522","pdf_url":"https://arxiv.org/pdf/2608.02522","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,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.02522","doi":"https://doi.org/10.48550/arxiv.2608.02522","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.02522","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,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.02522","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.02522","pdf_url":"https://arxiv.org/pdf/2608.02522","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,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G8402054218","display_name":"Graph coloring motivated by Hadwiger's conjecture","funder_award_id":"216071","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7172402385.pdf","grobid_xml":"https://content.openalex.org/works/W7172402385.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2279271104","https://openalex.org/W1599766299","https://openalex.org/W3011709781","https://openalex.org/W7172407383","https://openalex.org/W2115242161","https://openalex.org/W1532010022","https://openalex.org/W2283969291","https://openalex.org/W4416410637","https://openalex.org/W4416054906","https://openalex.org/W1980923667"],"abstract_inverted_index":{"A":[0],"famous":[1],"conjecture":[2,140],"of":[3,25,34,61,74,86,110,117,126,141,149,197,215,235,269],"Erd\u0151s":[4,150],"and":[5,38,81,132,143,151,154,273],"Hajnal":[6,152],"(1969)":[7],"states":[8],"that":[9,22,94,114,245],"for":[10,50,95,155,201,247,280],"every":[11,23,96,115,202,204,248],"integer":[12],"$g\\ge":[13,98],"4$":[14],"there":[15,100],"is":[16,101,182,227],"a":[17,32,59,67,102,107,124,139,147,163,169,212,228],"smallest":[18],"function":[19,103],"$f_g:\\mathbb{N}\\to\\mathbb{N}$":[20],"such":[21,113],"graph":[24,116,178,205],"chromatic":[26,35,118,127,185,194],"number":[27,36,119,128,195],"at":[28,40,120,129,134,217],"least":[29,41,121,130,135,218],"$f_g(k)$":[30],"contains":[31,123,211],"subgraph":[33,125,213],"$k$":[37,131],"girth":[39],"$g$.":[42,136],"So":[43],"far,":[44],"this":[45,90,167],"has":[46],"only":[47],"been":[48],"proved":[49],"$g=4$":[51],"by":[52,58,278],"R\u00f6dl":[53],"(1977),":[54],"with":[55,207,220],"$f_4(k)$":[56,161],"bounded":[57],"tower":[60,109],"height":[62,111],"$\u0398(k^2\\log":[63],"k)$.":[64],"We":[65,165,243],"exhibit":[66],"surprising":[68],"connection":[69],"between":[70],"finding":[71],"high-chromatic":[72],"subgraphs":[73],"large":[75,209],"odd-girth":[76,133,216],"(avoiding":[77],"short":[78],"odd":[79,87,97,236,271],"cycles)":[80],"lower-bounding":[82],"multicolor":[83,266],"Ramsey":[84,233,267],"numbers":[85,234,268],"cycles.":[88,237],"Using":[89],"connection,":[91],"we":[92],"prove":[93],"5$":[99],"$h_g:\\mathbb{N}\\to\\mathbb{N}$":[104],"growing":[105],"as":[106],"power":[108],"$\\frac{g-3}{2}$":[112],"$h_g(k)$":[122],"This":[137,258],"proves":[138],"Mohar":[142],"Wu":[144],"(2018),":[145],"addresses":[146],"question":[148],"(1975),":[153],"$g=5$":[156],"improves":[157],"R\u00f6dl's":[158],"bound":[159,231,264],"on":[160,232,265],"to":[162,168,176],"single-exponential.":[164],"extend":[166],"much":[170],"more":[171],"general":[172],"meta-theorem":[173],"which":[174],"applies":[175],"many":[177],"parameters:":[179],"if":[180],"$f$":[181],"the":[183,187,191,198,254,260,275],"fractional":[184],"number,":[186],"Hall":[188],"ratio,":[189],"or":[190],"strict":[192],"vector":[193],"(Lov\u00e1sz-Theta-function":[196],"complement),":[199],"then":[200],"$k,g\\in\\mathbb{N}$,":[203],"$G$":[206],"sufficiently":[208],"$f(G)$":[210],"$G'$":[214],"$g$":[219],"$f(G')\\ge":[221],"k$.":[222],"The":[223],"key":[224],"Ramsey-theoretic":[225],"ingredient":[226],"new":[229],"lower":[230,263],"For":[238],"$p\\ge":[239],"1$,":[240],"let":[241],"$\\mathcal{O}_p=\\{C_3,C_5,\\ldots,C_{2p+1}\\}$.":[242],"show":[244],"$R_k(\\mathcal{O}_p)\\ge(\\log^{(p-1)}k)^{k/3-o(k)}$":[246],"fixed":[249,270],"$p$,":[250],"where":[251],"$\\log^{(p-1)}$":[252],"denotes":[253],"$(p-1)$-fold":[255],"iterated":[256],"logarithm.":[257],"yields":[259],"first":[261],"superexponential":[262],"cycles,":[272],"extends":[274],"recent":[276],"breakthrough":[277],"OpenAI":[279],"triangles.":[281]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-05T00:00:00"}
