{"id":"https://openalex.org/W7212017199","doi":"https://doi.org/10.48550/arxiv.2609.08903","title":"On the classification of regular graphs with positive Lin-Lu-Yau curvature","display_name":"On the classification of regular graphs with positive Lin-Lu-Yau curvature","publication_year":2026,"publication_date":"2026-09-08","ids":{"openalex":"https://openalex.org/W7212017199","doi":"https://doi.org/10.48550/arxiv.2609.08903"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.08903","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.08903","pdf_url":"https://arxiv.org/pdf/2609.08903","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/2609.08903","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111143279","display_name":"George Brooks","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Brooks, George","raw_affiliation_strings":["University of South Carolina , Columbia , SC , USA","\u2016"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of South Carolina , Columbia , SC , USA","institution_ids":["https://openalex.org/I155781252"]},{"raw_affiliation_string":"\u2016","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089494566","display_name":"Nathanael Johnson","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Johnson, Nathanael","raw_affiliation_strings":["The Ohio State University , Columbus , OH , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Ohio State University , Columbus , OH , USA","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067520532","display_name":"William Linz","orcid":"https://orcid.org/0009-0006-0579-0576","observed_orcids":["https://orcid.org/0009-0006-0579-0576"]},"institutions":[{"id":"https://openalex.org/I94658018","display_name":"University of Memphis","ror":"https://ror.org/01cq23130","country_code":"US","type":"education","lineage":["https://openalex.org/I94658018"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Linz, William","raw_affiliation_strings":["University of Memphis , Memphis , TN , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Memphis , Memphis , TN , USA","institution_ids":["https://openalex.org/I94658018"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5147737389","display_name":"Xiaonan Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Liu, Xiaonan","raw_affiliation_strings":["Louisiana State University , LA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Louisiana State University , LA , USA","institution_ids":["https://openalex.org/I121820613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5146383599","display_name":"Linyuan Lu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lu, Linyuan","raw_affiliation_strings":["University of South Carolina , Columbia , SC , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of South Carolina , Columbia , SC , USA","institution_ids":["https://openalex.org/I155781252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5150974275","display_name":"Wynton Vaughn","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I8078737","display_name":"Clemson University","ror":"https://ror.org/037s24f05","country_code":"US","type":"education","lineage":["https://openalex.org/I8078737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vaughn, Wynton","raw_affiliation_strings":["Clemson University , Clemson , SC , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Clemson University , Clemson , SC , USA","institution_ids":["https://openalex.org/I8078737"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.002899999963119626,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.0010000000474974513,"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/d-regular-graphs","display_name":"d-regular graphs","score":0.8859999775886536},{"id":"https://openalex.org/keywords/graph-classification","display_name":"graph classification","score":0.6480000019073486},{"id":"https://openalex.org/keywords/diameter-bounds","display_name":"diameter bounds","score":0.6769999861717224},{"id":"https://openalex.org/keywords/bonnet-myers-theorem","display_name":"Bonnet-Myers theorem","score":0.9449999928474426},{"id":"https://openalex.org/keywords/cubic-graphs","display_name":"cubic graphs","score":0.9950000047683716},{"id":"https://openalex.org/keywords/planar-graphs","display_name":"planar graphs","score":0.7540000081062317},{"id":"https://openalex.org/keywords/discrete-curvature","display_name":"discrete curvature","score":0.5049999952316284}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7953000068664551},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.6606000065803528},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5764999985694885},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.521399974822998},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.43709999322891235},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4047999978065491},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4023999869823456},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.3986000120639801},{"id":"https://openalex.org/C133875400","wikidata":"https://www.wikidata.org/wiki/Q692823","display_name":"Strongly regular graph","level":5,"score":0.3411000072956085},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.30320000648498535},{"id":"https://openalex.org/C125792925","wikidata":"https://www.wikidata.org/wiki/Q3115604","display_name":"Outerplanar graph","level":5,"score":0.2953999936580658},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.27869999408721924}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.08903","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.08903","pdf_url":"https://arxiv.org/pdf/2609.08903","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.2609.08903","doi":"https://doi.org/10.48550/arxiv.2609.08903","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.08903","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.08903","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.08903","pdf_url":"https://arxiv.org/pdf/2609.08903","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":[{"id":"https://openalex.org/G8921292286","display_name":"RTG: Mathematical Foundation of Data Science at University of South Carolina","funder_award_id":"2038080","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320310846","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212017199.pdf","grobid_xml":"https://content.openalex.org/works/W7212017199.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4403780014","https://openalex.org/W4403786541"],"related_works":["https://openalex.org/W7128511646","https://openalex.org/W3214030788","https://openalex.org/W2584639272","https://openalex.org/W3206553724","https://openalex.org/W4400464939","https://openalex.org/W7220969414","https://openalex.org/W6979299635","https://openalex.org/W7167236677","https://openalex.org/W7220704761","https://openalex.org/W4400667682"],"abstract_inverted_index":{"We":[0,16,46,60],"prove":[1],"several":[2],"new":[3],"structural":[4],"and":[5],"classification":[6],"results":[7],"about":[8],"$d$-regular":[9,22,53],"graphs":[10],"with":[11,55],"positive":[12],"Lin--Lu--Yau":[13],"(LLY)":[14],"curvature.":[15],"show":[17,48],"that":[18,49],"any":[19],"positively":[20,43,51,63,71],"curved":[21,44,52,64,72],"graph":[23,54],"has":[24],"diameter":[25,35],"at":[26],"most":[27],"$2d-2$,":[28],"which":[29],"improves":[30],"the":[31,39],"previously":[32],"best":[33],"known":[34],"bound":[36],"obtained":[37],"from":[38],"Bonnet-Myers-type":[40],"theorem":[41],"for":[42],"graphs.":[45,75],"further":[47],"every":[50],"$d\\ge":[56],"3$":[57],"is":[58],"$3$-connected.":[59],"classify":[61],"all":[62,70],"$3$-regular":[65],"graphs,":[66],"as":[67,69],"well":[68],"regular":[73],"planar":[74]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-10T00:00:00"}
