{"id":"https://openalex.org/W7168408317","doi":"https://doi.org/10.48550/arxiv.2607.12461","title":"Local flag algebras","display_name":"Local flag algebras","publication_year":2026,"publication_date":"2026-07-14","ids":{"openalex":"https://openalex.org/W7168408317","doi":"https://doi.org/10.48550/arxiv.2607.12461"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2607.12461","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2607.12461","pdf_url":"https://arxiv.org/pdf/2607.12461","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2607.12461","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5141267862","display_name":"Eoin Davey","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Davey, Eoin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022330337","display_name":"Eoin Hurley","orcid":"https://orcid.org/0000-0001-6895-8061","observed_orcids":["https://orcid.org/0000-0001-6895-8061"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hurley, Eoin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075351819","display_name":"R\u00e9mi de Joannis de Verclos","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"de Verclos, R\u00e9mi de Joannis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019911064","display_name":"Ross J. Kang","orcid":"https://orcid.org/0000-0002-4219-593X","observed_orcids":["https://orcid.org/0000-0002-4219-593X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kang, Ross J.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5082781996","display_name":"Jan Volec","orcid":"https://orcid.org/0000-0002-5310-3797","observed_orcids":["https://orcid.org/0000-0002-5310-3797"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Volec, Jan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/flag-algebras","display_name":"flag algebras","score":0.8299999833106995},{"id":"https://openalex.org/keywords/extremal-graph-theory","display_name":"extremal graph theory","score":0.8090000152587891},{"id":"https://openalex.org/keywords/maximum-degree","display_name":"maximum degree","score":0.8220000267028809},{"id":"https://openalex.org/keywords/pentagon","display_name":"Pentagon","score":0.6650000214576721},{"id":"https://openalex.org/keywords/triangle-free-graphs","display_name":"triangle-free graphs","score":0.9959999918937683},{"id":"https://openalex.org/keywords/subgraph-counting","display_name":"subgraph counting","score":0.5590000152587891},{"id":"https://openalex.org/keywords/graph-density","display_name":"graph density","score":0.32899999618530273}],"concepts":[{"id":"https://openalex.org/C2776730729","wikidata":"https://www.wikidata.org/wiki/Q1392130","display_name":"Flag (linear algebra)","level":3,"score":0.7753000259399414},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7351999878883362},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5166000127792358},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4837999939918518},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4352000057697296},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4284999966621399},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4278999865055084},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3806999921798706},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37779998779296875},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.3521000146865845},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.33559998869895935},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.3330000042915344},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3228999972343445},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.31470000743865967},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.28130000829696655}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2607.12461","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2607.12461","pdf_url":"https://arxiv.org/pdf/2607.12461","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.2607.12461","doi":"https://doi.org/10.48550/arxiv.2607.12461","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.12461","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2607.12461","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2607.12461","pdf_url":"https://arxiv.org/pdf/2607.12461","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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3412787705","display_name":"Asymptotic triangle-free structure (3Free)","funder_award_id":"OCENW.M20.009","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G5093044862","display_name":null,"funder_award_id":"OCENW.M20","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G565383568","display_name":null,"funder_award_id":"024-002-003","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G8688676036","display_name":"On the edge: theory and techniques at the frontiers of edge-colouring","funder_award_id":"639.032.614","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321008","display_name":"Universiteit van Amsterdam","ror":"https://ror.org/04dkp9463"},{"id":"https://openalex.org/F4320321013","display_name":"Radboud Universiteit","ror":"https://ror.org/016xsfp80"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7168408317.pdf","grobid_xml":"https://content.openalex.org/works/W7168408317.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"introduce":[1],"local":[2],"flag":[3,9],"algebras,":[4],"a":[5,62,67],"variant":[6],"of":[7,59,69],"Razborov's":[8],"algebra":[10],"framework":[11,28],"in":[12,61],"which":[13],"densities":[14],"are":[15],"normalised":[16],"by":[17],"the":[18,24,30,35,47,57],"maximum":[19,48],"degree":[20],"$\u0394(G)$":[21],"rather":[22],"than":[23],"order":[25],"$|G|$.":[26],"The":[27],"supports":[29],"same":[31],"semidefinite-method":[32],"machinery":[33],"as":[34,66],"classical":[36],"version,":[37],"but":[38],"is":[39],"tailored":[40],"to":[41],"extremal":[42],"problems":[43],"that":[44],"scale":[45],"with":[46],"degree.":[49],"As":[50],"an":[51],"illustrative":[52],"first":[53],"application":[54],"we":[55],"bound":[56],"number":[58],"pentagons":[60],"triangle-free":[63],"graph":[64],"$G$":[65],"function":[68],"$|G|$":[70],"and":[71],"$\u0394(G)$.":[72]},"counts_by_year":[],"updated_date":"2026-10-15T10:00:46.086208","created_date":"2026-07-16T00:00:00"}