{"id":"https://openalex.org/W7208813232","doi":"https://doi.org/10.5281/zenodo.22343830","title":"A New Proof of the Four Color Theorem","display_name":"A New Proof of the Four Color Theorem","publication_year":2026,"publication_date":"2026-09-05","ids":{"openalex":"https://openalex.org/W7208813232","doi":"https://doi.org/10.5281/zenodo.22343830"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.22343830","doi":"https://doi.org/10.5281/zenodo.22343830","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22343830","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.22343830","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068191315","display_name":"Zhenxi Huang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I159948400","display_name":"Jinan University","ror":"https://ror.org/02xe5ns62","country_code":"CN","type":"education","lineage":["https://openalex.org/I159948400"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Huang, Zhenxi","raw_affiliation_strings":["Jinan University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jinan University","institution_ids":["https://openalex.org/I159948400"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5068191315"],"corresponding_institution_ids":["https://openalex.org/I159948400"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.8539999723434448,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.8539999723434448,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.060600001364946365,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.011800000444054604,"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/four-color-theorem","display_name":"four-color theorem","score":0.949999988079071},{"id":"https://openalex.org/keywords/map-coloring","display_name":"map coloring","score":0.8759999871253967},{"id":"https://openalex.org/keywords/inductive-proof","display_name":"inductive proof","score":0.7900000214576721},{"id":"https://openalex.org/keywords/planar-graphs","display_name":"planar graphs","score":0.7350000143051147},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"graph coloring","score":0.5289999842643738}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6988999843597412},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5564000010490417},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.448199987411499},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.42640000581741333},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38269999623298645},{"id":"https://openalex.org/C2778307483","wikidata":"https://www.wikidata.org/wiki/Q5149038","display_name":"Colored","level":2,"score":0.38040000200271606},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36820000410079956},{"id":"https://openalex.org/C171636804","wikidata":"https://www.wikidata.org/wiki/Q1149458","display_name":"Compactness theorem","level":4,"score":0.32659998536109924},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2948000133037567},{"id":"https://openalex.org/C146147875","wikidata":"https://www.wikidata.org/wiki/Q1144897","display_name":"Brouwer fixed-point theorem","level":3,"score":0.2815000116825104},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.27489998936653137},{"id":"https://openalex.org/C51658606","wikidata":"https://www.wikidata.org/wiki/Q512897","display_name":"Brooks' theorem","level":5,"score":0.2700999975204468},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2646999955177307},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.25589999556541443},{"id":"https://openalex.org/C36262787","wikidata":"https://www.wikidata.org/wiki/Q2294018","display_name":"Color model","level":4,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.22343830","doi":"https://doi.org/10.5281/zenodo.22343830","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22343830","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.22343831","doi":"https://doi.org/10.5281/zenodo.22343831","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22343831","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"doi:10.5281/zenodo.22343830","doi":"https://doi.org/10.5281/zenodo.22343830","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22343830","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"Four":[1,71],"Color":[2,72],"Theorem":[3,73],"states":[4],"that":[5,21],"every":[6],"finite":[7],"map":[8],"on":[9],"the":[10,34,56,70],"sphere":[11],"can":[12],"be":[13],"colored":[14],"with":[15],"at":[16],"most":[17],"four":[18],"colors":[19],"so":[20],"any":[22],"two":[23],"adjacent":[24],"regions":[25],"receive":[26],"different":[27],"colors.":[28],"In":[29],"this":[30,59],"paper,":[31],"we":[32],"study":[33],"theorem":[35],"from":[36],"a":[37,46,76],"topological":[38],"and":[39,44,78],"graph-theoretic":[40],"point":[41],"of":[42],"view":[43],"introduce":[45],"strengthened":[47],"boundary":[48],"coloring":[49],"property":[50,60],"for":[51,68],"disk":[52],"triangulations.":[53],"By":[54],"applying":[55],"inductive":[57,66],"hypothesis,":[58],"is":[61],"preserved.":[62],"This":[63],"provides":[64],"an":[65],"framework":[67],"proving":[69],"without":[74],"using":[75],"computer":[77],"exhaustion.":[79]},"counts_by_year":[],"updated_date":"2026-10-07T09:51:55.459714","created_date":"2026-09-06T00:00:00"}