{"id":"https://openalex.org/W1554387854","doi":"https://doi.org/10.37236/1458","title":"The Gr\u00f6tzsch Theorem for the Hypergraph of Maximal Cliques","display_name":"The Gr\u00f6tzsch Theorem for the Hypergraph of Maximal Cliques","publication_year":1999,"publication_date":"1999-06-07","ids":{"openalex":"https://openalex.org/W1554387854","doi":"https://doi.org/10.37236/1458","mag":"1554387854"},"language":"en","primary_location":{"id":"doi:10.37236/1458","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1458","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v6i1r26/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v6i1r26/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005993212","display_name":"Bojan Mohar","orcid":"https://orcid.org/0000-0002-7408-6148"},"institutions":[{"id":"https://openalex.org/I153976015","display_name":"University of Ljubljana","ror":"https://ror.org/05njb9z20","country_code":"SI","type":"education","lineage":["https://openalex.org/I153976015"]}],"countries":["SI"],"is_corresponding":true,"raw_author_name":"Bojan Mohar","raw_affiliation_strings":["University of Ljubljana"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Ljubljana","institution_ids":["https://openalex.org/I153976015"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083674096","display_name":"Riste \u0160krekovski","orcid":"https://orcid.org/0000-0001-6851-3214"},"institutions":[{"id":"https://openalex.org/I153976015","display_name":"University of Ljubljana","ror":"https://ror.org/05njb9z20","country_code":"SI","type":"education","lineage":["https://openalex.org/I153976015"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Riste Skrekovski","raw_affiliation_strings":["University of Ljubljana"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Ljubljana","institution_ids":["https://openalex.org/I153976015"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5005993212"],"corresponding_institution_ids":["https://openalex.org/I153976015"],"apc_list":null,"apc_paid":null,"fwci":1.6906,"has_fulltext":true,"cited_by_count":53,"citation_normalized_percentile":{"value":0.83262612,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"6","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9988999962806702,"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":0.9905999898910522,"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/hypergraph","display_name":"Hypergraph","score":0.8555822372436523},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.83770751953125},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8254730701446533},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.635193943977356},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.5495990514755249},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5136372447013855},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5043803453445435},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.4401451647281647},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4255374073982239},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07283931970596313}],"concepts":[{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.8555822372436523},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.83770751953125},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8254730701446533},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.635193943977356},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5495990514755249},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5136372447013855},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5043803453445435},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.4401451647281647},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4255374073982239},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07283931970596313},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.37236/1458","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1458","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v6i1r26/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.18.1364","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.18.1364","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ijp.si/ftp/pub/preprints/ps/98/pp631.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.28.7558","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.28.7558","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://www.ijp.si/pub/preprints/ps/98/pp631.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.43.9258","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.43.9258","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_6/PostScriptfiles/v6i1r26.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.46.5345","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.5345","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.sztaki.hu/mirrors/EMIS/journals/EJC/Volume_6/PDF/v6i1r26.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.636.3820","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.636.3820","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.imfm.si/preprinti/PDF/00631.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1458","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1458","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v6i1r26/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1554387854.pdf"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W345637930","https://openalex.org/W574460519","https://openalex.org/W1492343704","https://openalex.org/W1531267818","https://openalex.org/W1830275774","https://openalex.org/W2022408132","https://openalex.org/W2083560794","https://openalex.org/W2148360835","https://openalex.org/W4285719527","https://openalex.org/W4301890399"],"related_works":["https://openalex.org/W4376608589","https://openalex.org/W3138003926","https://openalex.org/W4300037846","https://openalex.org/W4281615795","https://openalex.org/W1701875187","https://openalex.org/W2990956612","https://openalex.org/W3084676277","https://openalex.org/W1606013690","https://openalex.org/W4293743430","https://openalex.org/W3006156235"],"abstract_inverted_index":{"In":[0],"this":[1,25],"paper,":[2],"we":[3],"extend":[4,24],"the":[5,11,53],"Gr\u00f6tzsch":[6],"Theorem":[7],"by":[8,30],"proving":[9,31],"that":[10,32],"clique":[12],"hypergraph":[13],"${\\cal":[14,33,48],"H}(G)$":[15,34,49],"of":[16,47,55],"every":[17,38],"planar":[18,39,42,57],"graph":[19,43],"is":[20,35,50],"3-colorable.":[21],"We":[22],"also":[23],"result":[26],"to":[27],"list":[28],"colorings":[29],"4-choosable":[36],"for":[37,52],"or":[40],"projective":[41],"$G$.":[44],"Finally,":[45],"4-choosability":[46],"established":[51],"class":[54],"locally":[56],"graphs":[58],"on":[59],"arbitrary":[60],"surfaces.":[61]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}