{"id":"https://openalex.org/W1984138826","doi":"https://doi.org/10.1016/0012-365x(83)90128-0","title":"Representing a planar graph by vertical lines joining different levels","display_name":"Representing a planar graph by vertical lines joining different levels","publication_year":1983,"publication_date":"1983-01-01","ids":{"openalex":"https://openalex.org/W1984138826","doi":"https://doi.org/10.1016/0012-365x(83)90128-0","mag":"1984138826"},"language":"en","primary_location":{"id":"doi:10.1016/0012-365x(83)90128-0","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(83)90128-0","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082527853","display_name":"Pierre Duchet","orcid":null},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"P. Duchet","raw_affiliation_strings":["Universit\u00e9 Pierre et Marie Curie, D\u00e9partment de Math\u00e9matiques (U.E.R. 48), 4 place Jussie, 75005 Paris, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Pierre et Marie Curie, D\u00e9partment de Math\u00e9matiques (U.E.R. 48), 4 place Jussie, 75005 Paris, France","institution_ids":["https://openalex.org/I39804081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108518802","display_name":"Yahya Ould Hamidoune","orcid":null},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Y. Hamidoune","raw_affiliation_strings":["Universit\u00e9 Pierre et Marie Curie, D\u00e9partment de Math\u00e9matiques (U.E.R. 48), 4 place Jussie, 75005 Paris, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Pierre et Marie Curie, D\u00e9partment de Math\u00e9matiques (U.E.R. 48), 4 place Jussie, 75005 Paris, France","institution_ids":["https://openalex.org/I39804081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052055459","display_name":"Michel Las Vergnas","orcid":null},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"M. Las Vergnas","raw_affiliation_strings":["Universit\u00e9 Pierre et Marie Curie, D\u00e9partment de Math\u00e9matiques (U.E.R. 48), 4 place Jussie, 75005 Paris, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Pierre et Marie Curie, D\u00e9partment de Math\u00e9matiques (U.E.R. 48), 4 place Jussie, 75005 Paris, France","institution_ids":["https://openalex.org/I39804081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109941799","display_name":"H. Meyniel","orcid":null},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"H. Meyniel","raw_affiliation_strings":["Universit\u00e9 Pierre et Marie Curie, D\u00e9partment de Math\u00e9matiques (U.E.R. 48), 4 place Jussie, 75005 Paris, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Pierre et Marie Curie, D\u00e9partment de Math\u00e9matiques (U.E.R. 48), 4 place Jussie, 75005 Paris, France","institution_ids":["https://openalex.org/I39804081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5082527853"],"corresponding_institution_ids":["https://openalex.org/I39804081"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":1.4907,"has_fulltext":false,"cited_by_count":67,"citation_normalized_percentile":{"value":0.80824373,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"46","issue":"3","first_page":"319","last_page":"321"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9657999873161316,"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/T12698","display_name":"3D Modeling in Geospatial Applications","score":0.9595999717712402,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8392211198806763},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.771530270576477},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.7281429171562195},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6943929195404053},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5741742253303528},{"id":"https://openalex.org/keywords/outerplanar-graph","display_name":"Outerplanar graph","score":0.48038631677627563},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.46575719118118286},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.42329761385917664},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36785799264907837},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.2295149564743042},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.16433563828468323},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09890380501747131},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07961887121200562}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8392211198806763},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.771530270576477},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.7281429171562195},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6943929195404053},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5741742253303528},{"id":"https://openalex.org/C125792925","wikidata":"https://www.wikidata.org/wiki/Q3115604","display_name":"Outerplanar graph","level":5,"score":0.48038631677627563},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.46575719118118286},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.42329761385917664},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36785799264907837},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2295149564743042},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.16433563828468323},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09890380501747131},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07961887121200562},{"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/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0012-365x(83)90128-0","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(83)90128-0","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3216500139","https://openalex.org/W3034858646","https://openalex.org/W4287758186","https://openalex.org/W3135899633","https://openalex.org/W3216105633","https://openalex.org/W2963028755","https://openalex.org/W1701875187","https://openalex.org/W2952675320","https://openalex.org/W4289674633","https://openalex.org/W2990956612"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":7},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}