{"id":"https://openalex.org/W2273638248","doi":"https://doi.org/10.37236/7888","title":"Planar Transitive Graphs","display_name":"Planar Transitive Graphs","publication_year":2018,"publication_date":"2018-10-05","ids":{"openalex":"https://openalex.org/W2273638248","doi":"https://doi.org/10.37236/7888","mag":"2273638248"},"language":"en","primary_location":{"id":"doi:10.37236/7888","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7888","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p8/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":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p8/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056612439","display_name":"Matthias Hamann","orcid":"https://orcid.org/0009-0007-9455-8580"},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"Matthias Hamann","raw_affiliation_strings":["Alfred Renyi Institute of Mathematics, Budapest","Alfr\u00e9d R\u00e9nyi Institute Of Mathematics, Budapest,"],"affiliations":[{"raw_affiliation_string":"Alfred Renyi Institute of Mathematics, Budapest","institution_ids":["https://openalex.org/I127817813"]},{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute Of Mathematics, Budapest,","institution_ids":["https://openalex.org/I127817813"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056612439"],"corresponding_institution_ids":["https://openalex.org/I127817813"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00488794,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"25","issue":"4","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":0.9988999962806702,"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"}},"topics":[{"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/T10849","display_name":"Finite Group Theory Research","score":0.9987999796867371,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.996399998664856,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cayley-graph","display_name":"Cayley graph","score":0.797282874584198},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7425976395606995},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6438822746276855},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.6238686442375183},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.6224014759063721},{"id":"https://openalex.org/keywords/transitive-reduction","display_name":"Transitive reduction","score":0.5759998559951782},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.5401858687400818},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5099204778671265},{"id":"https://openalex.org/keywords/homology","display_name":"Homology (biology)","score":0.4595543146133423},{"id":"https://openalex.org/keywords/vertex-transitive-graph","display_name":"Vertex-transitive graph","score":0.4484350085258484},{"id":"https://openalex.org/keywords/polyhedral-graph","display_name":"Polyhedral graph","score":0.4128251075744629},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3577224314212799},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.30448782444000244},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.18160060048103333},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.15450850129127502},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11731106042861938},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.09909409284591675}],"concepts":[{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.797282874584198},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7425976395606995},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6438822746276855},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.6238686442375183},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.6224014759063721},{"id":"https://openalex.org/C129691609","wikidata":"https://www.wikidata.org/wiki/Q3088151","display_name":"Transitive reduction","level":5,"score":0.5759998559951782},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5401858687400818},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5099204778671265},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.4595543146133423},{"id":"https://openalex.org/C113203676","wikidata":"https://www.wikidata.org/wiki/Q220997","display_name":"Vertex-transitive graph","level":5,"score":0.4484350085258484},{"id":"https://openalex.org/C91233654","wikidata":"https://www.wikidata.org/wiki/Q4555371","display_name":"Polyhedral graph","level":5,"score":0.4128251075744629},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3577224314212799},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.30448782444000244},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.18160060048103333},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.15450850129127502},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11731106042861938},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.09909409284591675},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/7888","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7888","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p8/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":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1511.08777","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1511.08777","pdf_url":"https://arxiv.org/pdf/1511.08777","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":null},{"id":"mag:2273638248","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1511.08777v2","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1511.08777","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1511.08777","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/7888","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7888","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p8/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":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2273638248.pdf","grobid_xml":"https://content.openalex.org/works/W2273638248.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1918884707","https://openalex.org/W1979038996","https://openalex.org/W1996128530","https://openalex.org/W2010142885","https://openalex.org/W2027884001","https://openalex.org/W2128904726","https://openalex.org/W2155552412","https://openalex.org/W2166832684","https://openalex.org/W2799004609","https://openalex.org/W2949279286","https://openalex.org/W2963820742","https://openalex.org/W6679301078"],"related_works":["https://openalex.org/W2962858507","https://openalex.org/W2094350827","https://openalex.org/W3098898780","https://openalex.org/W113487936","https://openalex.org/W2422178697","https://openalex.org/W2054586394","https://openalex.org/W2010253933","https://openalex.org/W1524718528","https://openalex.org/W2118075105","https://openalex.org/W2040250200","https://openalex.org/W2950502168","https://openalex.org/W2003293537","https://openalex.org/W2094832778","https://openalex.org/W3143238889","https://openalex.org/W2035379096","https://openalex.org/W2569447886","https://openalex.org/W3016862303","https://openalex.org/W2135429422","https://openalex.org/W2048298234","https://openalex.org/W1525343838"],"abstract_inverted_index":{"We":[0],"prove":[1,23],"that":[2,44,53],"the":[3,28],"first":[4],"homology":[5],"group":[6,30],"of":[7,31,38],"every":[8],"planar":[9,34,45,54],"locally":[10,32,55],"finite":[11,33,56],"transitive":[12,57],"graph":[13],"$G$":[14],"is":[15],"finitely":[16,48],"generated":[17],"as":[18],"an":[19],"$\\Aut(G)$-module":[20],"and":[21,50],"we":[22],"a":[24],"similar":[25],"result":[26],"for":[27],"fundamental":[29],"Cayley":[35],"graphs.":[36],"Corollaries":[37],"these":[39],"results":[40],"include":[41],"Droms's":[42],"theorem":[43,52],"groups":[46],"are":[47,59],"presented":[49],"Dunwoody's":[51],"graphs":[58],"accessible.":[60]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}