{"id":"https://openalex.org/W2603976564","doi":"https://doi.org/10.37236/6992","title":"A Characterization of Circle Graphs in Terms of Multimatroid Representations","display_name":"A Characterization of Circle Graphs in Terms of Multimatroid Representations","publication_year":2020,"publication_date":"2020-01-24","ids":{"openalex":"https://openalex.org/W2603976564","doi":"https://doi.org/10.37236/6992","mag":"2603976564"},"language":"en","primary_location":{"id":"doi:10.37236/6992","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6992","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i1p25/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/v27i1p25/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057971093","display_name":"Robert Brijder","orcid":"https://orcid.org/0000-0002-8912-1735"},"institutions":[{"id":"https://openalex.org/I878454856","display_name":"Hasselt University","ror":"https://ror.org/04nbhqj75","country_code":"BE","type":"education","lineage":["https://openalex.org/I878454856"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Robert Brijder","raw_affiliation_strings":["Hasselt University","University of Hasselt >  >  >  >"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hasselt University","institution_ids":["https://openalex.org/I878454856"]},{"raw_affiliation_string":"University of Hasselt >  >  >  >","institution_ids":["https://openalex.org/I878454856"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066749771","display_name":"Lorenzo Traldi","orcid":"https://orcid.org/0000-0003-1097-2818"},"institutions":[{"id":"https://openalex.org/I184759092","display_name":"Lafayette College","ror":"https://ror.org/036n0x007","country_code":"US","type":"education","lineage":["https://openalex.org/I184759092"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lorenzo Traldi","raw_affiliation_strings":["Lafayette College","Lafayette Coll"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lafayette College","institution_ids":["https://openalex.org/I184759092"]},{"raw_affiliation_string":"Lafayette Coll","institution_ids":["https://openalex.org/I184759092"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00626291,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"1","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":0.9983999729156494,"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":0.9983999729156494,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9858999848365784,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.980400025844574,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/matroid","display_name":"Matroid","score":0.8896770477294922},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8466424942016602},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6880004405975342},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.5147209763526917},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5109750032424927},{"id":"https://openalex.org/keywords/simple-graph","display_name":"Simple graph","score":0.4993138313293457},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4629334807395935},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.45778077840805054},{"id":"https://openalex.org/keywords/circle-graph","display_name":"Circle graph","score":0.44004812836647034},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.4245503842830658},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17643412947654724},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.09272441267967224},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.0924852192401886}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.8896770477294922},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8466424942016602},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6880004405975342},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5147209763526917},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5109750032424927},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.4993138313293457},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4629334807395935},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.45778077840805054},{"id":"https://openalex.org/C171528893","wikidata":"https://www.wikidata.org/wiki/Q5121450","display_name":"Circle graph","level":5,"score":0.44004812836647034},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.4245503842830658},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17643412947654724},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.09272441267967224},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0924852192401886},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/6992","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6992","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i1p25/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:1703.05960","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1703.05960","pdf_url":"https://arxiv.org/pdf/1703.05960","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":null,"raw_type":"text"},{"id":"mag:2603976564","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1703.05960.pdf","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":"pmh:oai:documentserver.uhasselt.be:1942/30771","is_oa":true,"landing_page_url":"http://hdl.handle.net/1942/30771","pdf_url":null,"source":{"id":"https://openalex.org/S4306401926","display_name":"Document Server@UHasselt (UHasselt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I878454856","host_organization_name":"Hasselt University","host_organization_lineage":["https://openalex.org/I878454856"],"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":"","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1703.05960","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1703.05960","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-journal"}],"best_oa_location":{"id":"doi:10.37236/6992","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6992","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i1p25/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":[{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2603976564.pdf","grobid_xml":"https://content.openalex.org/works/W2603976564.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W45625111","https://openalex.org/W96319801","https://openalex.org/W1501742082","https://openalex.org/W1790221062","https://openalex.org/W1846948956","https://openalex.org/W1972360724","https://openalex.org/W1973469272","https://openalex.org/W1987044417","https://openalex.org/W2004308928","https://openalex.org/W2006383151","https://openalex.org/W2013445331","https://openalex.org/W2033956728","https://openalex.org/W2038711832","https://openalex.org/W2046436885","https://openalex.org/W2050872937","https://openalex.org/W2059123040","https://openalex.org/W2067038884","https://openalex.org/W2069455721","https://openalex.org/W2075373454","https://openalex.org/W2090799803","https://openalex.org/W2135861887","https://openalex.org/W2165495371","https://openalex.org/W2257835027","https://openalex.org/W2502030701","https://openalex.org/W2883247096","https://openalex.org/W2963031626","https://openalex.org/W2964308755","https://openalex.org/W3101343723","https://openalex.org/W3139860308","https://openalex.org/W4231868828","https://openalex.org/W4237496336"],"related_works":["https://openalex.org/W2082076551","https://openalex.org/W3023466182","https://openalex.org/W1157673095","https://openalex.org/W3014765870","https://openalex.org/W2798053658","https://openalex.org/W2955957317","https://openalex.org/W2166753078","https://openalex.org/W2002853337","https://openalex.org/W3081812744","https://openalex.org/W1932319380","https://openalex.org/W2989754768","https://openalex.org/W1764280158","https://openalex.org/W2582851771","https://openalex.org/W1963843244","https://openalex.org/W1987235188","https://openalex.org/W163819639","https://openalex.org/W2241920064","https://openalex.org/W2338634437","https://openalex.org/W2130452056","https://openalex.org/W1545507519"],"abstract_inverted_index":{"The":[0,38],"isotropic":[1,17],"matroid":[2,13,102],"$M[IAS(G)]$":[3,23,42,63],"of":[4,19,34,41,56,62,68],"a":[5,11,75,87],"looped":[6],"simple":[7],"graph":[8,89,120],"$G$":[9,85],"is":[10,24,43,47,64,74,86,99],"binary":[12],"equivalent":[14],"to":[15,53,66],"the":[16,54,59,71,126],"system":[18],"$G$.":[20,57],"In":[21,79],"general,":[22],"not":[25],"regular,":[26],"so":[27],"it":[28,46],"cannot":[29],"be":[30],"represented":[31],"over":[32],"fields":[33],"characteristic":[35],"$\\neq":[36],"2$.":[37],"ground":[39,104],"set":[40,105],"denoted":[44,77],"$W(G)$;":[45],"partitioned":[48],"into":[49],"3-element":[50],"subsets":[51],"corresponding":[52],"vertices":[55],"When":[58],"rank":[60],"function":[61],"restricted":[65],"subtransversals":[67],"this":[69,80,114],"partition,":[70],"resulting":[72],"structure":[73],"multimatroid":[76],"$\\mathcal{Z}_{3}(G)$.":[78],"paper":[81],"we":[82],"prove":[83],"that":[84,122],"circle":[88,119],"if":[90,93],"and":[91],"only":[92],"for":[94],"every":[95],"field":[96],"$\\mathbb{F}$,":[97],"there":[98],"an":[100],"$\\mathbb{F}$-representable":[101],"with":[103,116],"$W(G)$,":[106],"which":[107],"defines":[108],"$\\mathcal{Z}_{3}(G)$":[109],"by":[110],"restriction.":[111],"We":[112],"connect":[113],"characterization":[115],"several":[117],"other":[118],"characterizations":[121],"have":[123],"appeared":[124],"in":[125],"literature.":[127]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
