{"id":"https://openalex.org/W7223701532","doi":"https://doi.org/10.48550/arxiv.2610.32677","title":"Sharp asymmetric vertex-Ramsey properties of graphs","display_name":"Sharp asymmetric vertex-Ramsey properties of graphs","publication_year":2026,"publication_date":"2026-10-23","ids":{"openalex":"https://openalex.org/W7223701532","doi":"https://doi.org/10.48550/arxiv.2610.32677"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.32677","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32677","pdf_url":"https://arxiv.org/pdf/2610.32677","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":null,"license_id":null,"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/2610.32677","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101853609","display_name":"Robert Hancock","orcid":"https://orcid.org/0000-0002-1548-5974","observed_orcids":["https://orcid.org/0000-0002-1548-5974"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hancock, Robert","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111421801","display_name":"Joseph Hyde","orcid":"https://orcid.org/0000-0002-1895-5791","observed_orcids":["https://orcid.org/0000-0002-1895-5791"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hyde, Joseph","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5119999367","display_name":"Ma\u00ebl Kupperschmitt","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I124357947","display_name":"University of London","ror":"https://ror.org/04cw6st05","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947"]},{"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"]},{"id":"https://openalex.org/I98259816","display_name":"Birkbeck, University of London","ror":"https://ror.org/02mb95055","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I98259816"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Kupperschmitt, Mael","raw_affiliation_strings":["Mathematical Institute , University of Oxford , Woodstock Road , Oxford , OX2 6GG , UK","School of Computing and Mathematical Sciences , Birkbeck , University of London , Malet St , London WC1E 7HX , UK,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute , University of Oxford , Woodstock Road , Oxford , OX2 6GG , UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"School of Computing and Mathematical Sciences , Birkbeck , University of London , Malet St , London WC1E 7HX , UK,","institution_ids":["https://openalex.org/I124357947","https://openalex.org/I98259816"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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/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"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/binomial-random-graphs","display_name":"binomial random graphs","score":0.8539999723434448},{"id":"https://openalex.org/keywords/sharp-threshold","display_name":"sharp threshold","score":0.7799999713897705},{"id":"https://openalex.org/keywords/balanced-graphs","display_name":"balanced graphs","score":0.5070000290870667},{"id":"https://openalex.org/keywords/hypergraphs","display_name":"hypergraphs","score":0.7049999833106995},{"id":"https://openalex.org/keywords/random-graphs","display_name":"random graphs","score":0.3400000035762787}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7335000038146973},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6414999961853027},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.5620999932289124},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5078999996185303},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48249998688697815},{"id":"https://openalex.org/C2781315470","wikidata":"https://www.wikidata.org/wiki/Q193623","display_name":"Binomial (polynomial)","level":2,"score":0.4359000027179718},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.4032000005245209},{"id":"https://openalex.org/C8554925","wikidata":"https://www.wikidata.org/wiki/Q3893853","display_name":"Split graph","level":5,"score":0.28929999470710754},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.2831000089645386},{"id":"https://openalex.org/C59824394","wikidata":"https://www.wikidata.org/wiki/Q5141281","display_name":"Cograph","level":5,"score":0.27869999408721924},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.2556999921798706}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.32677","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32677","pdf_url":"https://arxiv.org/pdf/2610.32677","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.32677","doi":"https://doi.org/10.48550/arxiv.2610.32677","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.32677","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:2610.32677","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32677","pdf_url":"https://arxiv.org/pdf/2610.32677","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223701532.pdf","grobid_xml":"https://content.openalex.org/works/W7223701532.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7166664617","https://openalex.org/W2527689252","https://openalex.org/W1970285613","https://openalex.org/W2168572475","https://openalex.org/W2047452808","https://openalex.org/W2271972529","https://openalex.org/W7033457329","https://openalex.org/W7096012691","https://openalex.org/W3166161324","https://openalex.org/W2885077188"],"abstract_inverted_index":{"In":[0,34,51],"1992,":[1],"\u0141uczak,":[2],"Ruci\u0144ski":[3],"and":[4,37,74],"Voigt":[5],"showed":[6,39,54],"that":[7,55],"for":[8,44,56,93],"any":[9,57],"graph":[10,28],"$H$,":[11],"a":[12,47,68],"parameter":[13,69],"$m_1(H)$":[14],"-":[15,19],"called":[16],"the":[17,21,25,31,77,83,101],"1-density":[18],"governs":[20,76],"threshold":[22,41,78,90],"at":[23,79],"which":[24,80],"binomial":[26],"random":[27],"$G(n,p)$":[29,81],"inherits":[30,82],"vertex-Ramsey":[32,85],"property.":[33,86],"2000,":[35],"Friedgut":[36],"Krivelevich":[38],"this":[40,89],"is":[42,91],"sharp":[43,92],"graphs":[45,58,94],"satisfying":[46],"natural":[48,96],"balancedness":[49,97],"condition.":[50],"1996,":[52],"Kreuter":[53],"$H_1,":[59],"\\ldots,":[60],"H_r$":[61],"with":[62],"$m_1(H_1)":[63],"\\geq":[64,66],"\\cdots":[65],"m_1(H_r)$,":[67],"dependent":[70],"only":[71],"on":[72],"$H_1$":[73],"$H_2$":[75],"`asymmetric'":[84],"We":[87],"prove":[88],"respecting":[95],"conditions,":[98],"including":[99],"in":[100],"analogous":[102],"hypergraph":[103],"setting.":[104]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-27T00:00:00"}
