{"id":"https://openalex.org/W1983580040","doi":"https://doi.org/10.1007/s00454-012-9400-1","title":"Triangle Contact Representations and Duality","display_name":"Triangle Contact Representations and Duality","publication_year":2012,"publication_date":"2012-02-15","ids":{"openalex":"https://openalex.org/W1983580040","doi":"https://doi.org/10.1007/s00454-012-9400-1","mag":"1983580040"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-012-9400-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-012-9400-1","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9400-1.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9400-1.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023564551","display_name":"Daniel Gon\u00e7alves","orcid":"https://orcid.org/0000-0003-3228-9622"},"institutions":[{"id":"https://openalex.org/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Daniel Gon\u00e7alves","raw_affiliation_strings":["Universit\u00e9 Montpellier 2, LIRMM, CNRS, 161 rue Ada, 34095, Montpellier Cedex 5, France#TAB#"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Montpellier 2, LIRMM, CNRS, 161 rue Ada, 34095, Montpellier Cedex 5, France#TAB#","institution_ids":["https://openalex.org/I19894307","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063411955","display_name":"Benjamin L\u00e9v\u00eaque","orcid":null},"institutions":[{"id":"https://openalex.org/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Benjamin L\u00e9v\u00eaque","raw_affiliation_strings":["Universit\u00e9 Montpellier 2, LIRMM, CNRS, 161 rue Ada, 34095, Montpellier Cedex 5, France#TAB#"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Montpellier 2, LIRMM, CNRS, 161 rue Ada, 34095, Montpellier Cedex 5, France#TAB#","institution_ids":["https://openalex.org/I19894307","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002340831","display_name":"Alexandre Pinlou","orcid":"https://orcid.org/0000-0002-3116-3019"},"institutions":[{"id":"https://openalex.org/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alexandre Pinlou","raw_affiliation_strings":["Universit\u00e9 Montpellier 2, LIRMM, CNRS, 161 rue Ada, 34095, Montpellier Cedex 5, France#TAB#"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Montpellier 2, LIRMM, CNRS, 161 rue Ada, 34095, Montpellier Cedex 5, France#TAB#","institution_ids":["https://openalex.org/I19894307","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5023564551"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I19894307"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":12.1849,"has_fulltext":true,"cited_by_count":34,"citation_normalized_percentile":{"value":0.98335509,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"48","issue":"1","first_page":"239","last_page":"254"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9939000010490417,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9599000215530396,"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/combinatorics","display_name":"Combinatorics","score":0.8128867149353027},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7421555519104004},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.6341657042503357},{"id":"https://openalex.org/keywords/dual-graph","display_name":"Dual graph","score":0.544670820236206},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.48314139246940613},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.48014897108078003},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4630591571331024},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.4559522271156311},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4502807855606079},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4407691955566406},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4215867221355438},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3056768774986267},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0801527202129364}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8128867149353027},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7421555519104004},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.6341657042503357},{"id":"https://openalex.org/C169827030","wikidata":"https://www.wikidata.org/wiki/Q2294516","display_name":"Dual graph","level":4,"score":0.544670820236206},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.48314139246940613},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.48014897108078003},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4630591571331024},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.4559522271156311},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4502807855606079},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4407691955566406},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4215867221355438},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3056768774986267},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0801527202129364},{"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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":2,"locations":[{"id":"doi:10.1007/s00454-012-9400-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-012-9400-1","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9400-1.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:HAL:lirmm-00715024v1","is_oa":false,"landing_page_url":"https://hal-lirmm.ccsd.cnrs.fr/lirmm-00715024","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete and Computational Geometry, 2012, 48 (1), pp.239-254. ⟨10.1007/s00454-012-9400-1⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.1007/s00454-012-9400-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-012-9400-1","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9400-1.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1415295610","display_name":"GRAphs through TOpological Structures","funder_award_id":"ANR-09-JCJC-0041","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1983580040.pdf","grobid_xml":"https://content.openalex.org/works/W1983580040.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1490017425","https://openalex.org/W1574212655","https://openalex.org/W1829919271","https://openalex.org/W1983547967","https://openalex.org/W2015594715","https://openalex.org/W2053876549","https://openalex.org/W2057600466","https://openalex.org/W2066423045","https://openalex.org/W2083176195","https://openalex.org/W2085823872","https://openalex.org/W2109558467","https://openalex.org/W2116670716","https://openalex.org/W2130702552","https://openalex.org/W2152799810","https://openalex.org/W2166735327","https://openalex.org/W2169775261","https://openalex.org/W2176056854","https://openalex.org/W2498084162","https://openalex.org/W2768011086"],"related_works":["https://openalex.org/W2371953206","https://openalex.org/W4300508906","https://openalex.org/W71032323","https://openalex.org/W1719252778","https://openalex.org/W4295995756","https://openalex.org/W2140952994","https://openalex.org/W2400746548","https://openalex.org/W2054102712","https://openalex.org/W4280629867","https://openalex.org/W4226175138"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}