{"id":"https://openalex.org/W2071725273","doi":"https://doi.org/10.1002/jgt.20554","title":"The plane-width of graphs","display_name":"The plane-width of graphs","publication_year":2011,"publication_date":"2011-02-01","ids":{"openalex":"https://openalex.org/W2071725273","doi":"https://doi.org/10.1002/jgt.20554","mag":"2071725273"},"language":"en","primary_location":{"id":"doi:10.1002/jgt.20554","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.20554","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0812.4346","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Marcin Kami\u0144ski","orcid":null},"institutions":[{"id":"https://openalex.org/I132053463","display_name":"Universit\u00e9 Libre de Bruxelles","ror":"https://ror.org/01r9htc13","country_code":"BE","type":"education","lineage":["https://openalex.org/I132053463"]},{"id":"https://openalex.org/I4210130966","display_name":"National Research Fund Luxembourg","ror":"https://ror.org/039z13y21","country_code":"LU","type":"nonprofit","lineage":["https://openalex.org/I4210130966"]}],"countries":["BE","LU"],"is_corresponding":true,"raw_author_name":"Marcin Kami\u0144ski","raw_affiliation_strings":["Departement D'informatique Universite Libre De Bruxelles Bruxelles, Belgium","Marcin Kamin\u0301ski is Charge\u0301e de Recherches du F.R.S.\u2014FNRS"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departement D'informatique Universite Libre De Bruxelles Bruxelles, Belgium","institution_ids":["https://openalex.org/I132053463"]},{"raw_affiliation_string":"Marcin Kamin\u0301ski is Charge\u0301e de Recherches du F.R.S.\u2014FNRS","institution_ids":["https://openalex.org/I4210130966"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Paul Medvedev","orcid":null},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Paul Medvedev","raw_affiliation_strings":["Department of Computer Science University of Toronto, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science University of Toronto, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":null,"display_name":"Martin Milani\u010d","orcid":null},"institutions":[{"id":"https://openalex.org/I118905719","display_name":"University of Primorska","ror":"https://ror.org/05xefg082","country_code":"SI","type":"education","lineage":["https://openalex.org/I118905719"]}],"countries":["SI"],"is_corresponding":true,"raw_author_name":"Martin Milani\u010d","raw_affiliation_strings":["Famnit and Pint University of Primorska, Koper, Slovenia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Famnit and Pint University of Primorska, Koper, Slovenia","institution_ids":["https://openalex.org/I118905719"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I118905719","https://openalex.org/I132053463","https://openalex.org/I185261750","https://openalex.org/I4210130966"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":0.299,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.60747113,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"68","issue":"3","first_page":"229","last_page":"245"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.5116000175476074,"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":0.5116000175476074,"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":0.23119999468326569,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.18359999358654022,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/wheel-graph","display_name":"Wheel graph","score":0.566100001335144},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.5569000244140625},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5568000078201294},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5094000101089478},{"id":"https://openalex.org/keywords/windmill-graph","display_name":"Windmill graph","score":0.4345000088214874},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.3944999873638153},{"id":"https://openalex.org/keywords/geometric-graph-theory","display_name":"Geometric graph theory","score":0.374099999666214},{"id":"https://openalex.org/keywords/bound-graph","display_name":"Bound graph","score":0.35600000619888306},{"id":"https://openalex.org/keywords/independent-set","display_name":"Independent set","score":0.3555999994277954}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8325999975204468},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7842000126838684},{"id":"https://openalex.org/C148364342","wikidata":"https://www.wikidata.org/wiki/Q948887","display_name":"Wheel graph","level":5,"score":0.566100001335144},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5569000244140625},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5568000078201294},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5094000101089478},{"id":"https://openalex.org/C73380178","wikidata":"https://www.wikidata.org/wiki/Q8024306","display_name":"Windmill graph","level":5,"score":0.4345000088214874},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41130000352859497},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.3944999873638153},{"id":"https://openalex.org/C173547177","wikidata":"https://www.wikidata.org/wiki/Q1503271","display_name":"Geometric graph theory","level":5,"score":0.374099999666214},{"id":"https://openalex.org/C121134508","wikidata":"https://www.wikidata.org/wiki/Q4949882","display_name":"Bound graph","level":5,"score":0.35600000619888306},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.3555999994277954},{"id":"https://openalex.org/C128067373","wikidata":"https://www.wikidata.org/wiki/Q1415372","display_name":"Path graph","level":5,"score":0.3133000135421753},{"id":"https://openalex.org/C168291704","wikidata":"https://www.wikidata.org/wiki/Q902252","display_name":"Complement graph","level":5,"score":0.30640000104904175},{"id":"https://openalex.org/C14201764","wikidata":"https://www.wikidata.org/wiki/Q1205074","display_name":"Symmetric graph","level":5,"score":0.30410000681877136},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2833999991416931},{"id":"https://openalex.org/C18819970","wikidata":"https://www.wikidata.org/wiki/Q3035340","display_name":"Butterfly graph","level":5,"score":0.2766000032424927},{"id":"https://openalex.org/C56783289","wikidata":"https://www.wikidata.org/wiki/Q3115556","display_name":"Distance-regular graph","level":5,"score":0.27630001306533813},{"id":"https://openalex.org/C161677786","wikidata":"https://www.wikidata.org/wiki/Q2478475","display_name":"Neighbourhood (mathematics)","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.27219998836517334},{"id":"https://openalex.org/C167750561","wikidata":"https://www.wikidata.org/wiki/Q1789512","display_name":"Critical graph","level":5,"score":0.2685000002384186},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.2630000114440918},{"id":"https://openalex.org/C7036158","wikidata":"https://www.wikidata.org/wiki/Q3385162","display_name":"Graph homomorphism","level":5,"score":0.2603999972343445},{"id":"https://openalex.org/C130184317","wikidata":"https://www.wikidata.org/wiki/Q3115549","display_name":"Unit disk graph","level":4,"score":0.25679999589920044},{"id":"https://openalex.org/C70488441","wikidata":"https://www.wikidata.org/wiki/Q5504427","display_name":"Friendship graph","level":5,"score":0.25130000710487366},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.2502000033855438}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1002/jgt.20554","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.20554","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0812.4346","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0812.4346","pdf_url":"https://arxiv.org/pdf/0812.4346","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,"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":"pmh:oai:dipot.ulb.ac.be:2013/70724","is_oa":false,"landing_page_url":"https://dipot.ulb.ac.be/dspace/bitstream/2013/70724/3/70724.pdf","pdf_url":"https://dipot.ulb.ac.be/dspace/bitstream/2013/70724/3/70724.pdf","source":{"id":"https://openalex.org/S4306401063","display_name":"D\u00e9p\u00f4t institutionnel de l'Universit\u00e9 libre de Bruxelles (Universit\u00e9 Libre de Bruxelles)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I132053463","host_organization_name":"Universit\u00e9 Libre de Bruxelles","host_organization_lineage":["https://openalex.org/I132053463"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of graph theory, 68 (3","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0812.4346","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0812.4346","pdf_url":"https://arxiv.org/pdf/0812.4346","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,"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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W73304290","https://openalex.org/W1526979981","https://openalex.org/W1807179603","https://openalex.org/W2011847656","https://openalex.org/W2018931513","https://openalex.org/W2035336359","https://openalex.org/W2055789678","https://openalex.org/W2072645091","https://openalex.org/W2082249316","https://openalex.org/W2086892639","https://openalex.org/W2094160323","https://openalex.org/W2099229992","https://openalex.org/W2105749797","https://openalex.org/W2106471982","https://openalex.org/W2130738665","https://openalex.org/W4229970255","https://openalex.org/W4247161715"],"related_works":[],"abstract_inverted_index":{"Map":[0],"the":[1,12,32,36,51,69,74,81],"vertices":[2,18],"of":[3,11,28,35,38,53,76],"a":[4,29,48,54],"graph":[5,30,55],"to":[6,64],"(not":[7],"necessarily":[8],"distinct)":[9],"points":[10],"plane":[13],"so":[14],"that":[15],"two":[16],"adjacent":[17],"are":[19],"mapped":[20],"at":[21],"least":[22],"unit":[23,78],"distance":[24],"apart.":[25],"The":[26],"plane-width":[27,52],"is":[31],"minimum":[33],"diameter":[34],"image":[37],"its":[39,57],"vertex":[40],"set":[41],"over":[42],"all":[43],"such":[44],"mappings.":[45],"We":[46,60],"establish":[47],"relation":[49],"between":[50],"and":[56,73],"chromatic":[58,71],"number.":[59],"also":[61],"connect":[62],"it":[63],"other":[65],"well-known":[66],"areas,":[67],"including":[68],"circular":[70],"number":[72],"problem":[75],"packing":[77],"discs":[79],"in":[80],"plane.":[82],"\u00a9":[83],"2011":[84,93],"Wiley":[85],"Periodicals,":[86],"Inc.":[87],"J":[88],"Graph":[89],"Theory":[90],"68:":[91],"229-245,":[92]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2016-06-24T00:00:00"}