{"id":"https://openalex.org/W2188476072","doi":"https://doi.org/10.1142/s0218195915500168","title":"3-Colorability of Pseudo-Triangulations","display_name":"3-Colorability of Pseudo-Triangulations","publication_year":2015,"publication_date":"2015-12-01","ids":{"openalex":"https://openalex.org/W2188476072","doi":"https://doi.org/10.1142/s0218195915500168","mag":"2188476072"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195915500168","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195915500168","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry & Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://upcommons.upc.edu/bitstream/2117/85279/1/3colorPPT.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091823049","display_name":"Oswin Aichholzer","orcid":"https://orcid.org/0000-0002-2364-0583"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Oswin Aichholzer","raw_affiliation_strings":["Institute for Software Technology, Graz University of Technology, Inffeldgasse 16b/II, Graz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Software Technology, Graz University of Technology, Inffeldgasse 16b/II, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065108210","display_name":"Franz Aurenhammer","orcid":null},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Franz Aurenhammer","raw_affiliation_strings":["Institute for Theoretical Computer Science, Graz University of Technology, Inffeldgasse 16b/I, Graz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Computer Science, Graz University of Technology, Inffeldgasse 16b/I, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103249365","display_name":"Thomas Hackl","orcid":"https://orcid.org/0000-0002-9875-9415"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Thomas Hackl","raw_affiliation_strings":["Institute for Software Technology, Graz University of Technology, Inffeldgasse 16b/II, Graz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Software Technology, Graz University of Technology, Inffeldgasse 16b/II, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032873622","display_name":"Clemens Huemer","orcid":"https://orcid.org/0000-0001-7557-0823"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Clemens Huemer","raw_affiliation_strings":["Departament de Matem\u00e0tica Alicada IV, Universitat Polit\u00e8cnica de Catalunya BarcelonaTech, C. Esteve Terradas 5, Castelldefels, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tica Alicada IV, Universitat Polit\u00e8cnica de Catalunya BarcelonaTech, C. Esteve Terradas 5, Castelldefels, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050197344","display_name":"Alexander Pilz","orcid":"https://orcid.org/0000-0002-6059-1821"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Alexander Pilz","raw_affiliation_strings":["Institute for Software Technology, Graz University of Technology, Inffeldgasse 16b/II, Graz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Software Technology, Graz University of Technology, Inffeldgasse 16b/II, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073288056","display_name":"Birgit Vogtenhuber","orcid":"https://orcid.org/0000-0002-7166-4467"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Birgit Vogtenhuber","raw_affiliation_strings":["Institute for Software Technology, Graz University of Technology, Inffeldgasse 16b/II, Graz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Software Technology, Graz University of Technology, Inffeldgasse 16b/II, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7058,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.74789971,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"25","issue":"04","first_page":"283","last_page":"298"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9987999796867371,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9958000183105469,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.814239501953125},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7862311601638794},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6149794459342957},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5667846202850342},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.5505368113517761},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5452731847763062},{"id":"https://openalex.org/keywords/face","display_name":"Face (sociological concept)","score":0.5179139971733093},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4785250425338745},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4428150951862335},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.41973876953125}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.814239501953125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7862311601638794},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6149794459342957},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5667846202850342},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.5505368113517761},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5452731847763062},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.5179139971733093},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4785250425338745},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4428150951862335},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.41973876953125},{"id":"https://openalex.org/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218195915500168","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195915500168","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry & Applications","raw_type":"journal-article"},{"id":"pmh:oai:upcommons.upc.edu:2117/85279","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/85279","pdf_url":"https://upcommons.upc.edu/bitstream/2117/85279/1/3colorPPT.pdf","source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:upcommons.upc.edu:2117/85279","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/85279","pdf_url":"https://upcommons.upc.edu/bitstream/2117/85279/1/3colorPPT.pdf","source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3013877478","display_name":null,"funder_award_id":"P23629-N18","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G406562094","display_name":null,"funder_award_id":"I 648-N18","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G6696703831","display_name":"EuroGIGA_Erd\u00f6s-Szekeres type problems for colored point sets and compatible graphs","funder_award_id":"I 648","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320310430","display_name":"TU Graz, Internationale Beziehungen und Mobilit\u00e4tsprogramme","ror":"https://ror.org/00d7xrm67"},{"id":"https://openalex.org/F4320321004","display_name":"\u00d6sterreichischen Akademie der Wissenschaften","ror":"https://ror.org/03anc3s24"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320338080","display_name":"European Social Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2188476072.pdf","grobid_xml":"https://content.openalex.org/works/W2188476072.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1512380301","https://openalex.org/W1531267818","https://openalex.org/W1559830328","https://openalex.org/W1969310879","https://openalex.org/W1981455469","https://openalex.org/W1996435735","https://openalex.org/W2022779815","https://openalex.org/W2083084150","https://openalex.org/W2089708856","https://openalex.org/W2134153007","https://openalex.org/W2160347332","https://openalex.org/W2953304270","https://openalex.org/W3103588612"],"related_works":["https://openalex.org/W4237277701","https://openalex.org/W2121424666","https://openalex.org/W4301250310","https://openalex.org/W2055420561","https://openalex.org/W2067700950","https://openalex.org/W1669998927","https://openalex.org/W2371138613","https://openalex.org/W3162039195","https://openalex.org/W2048963458","https://openalex.org/W43109613"],"abstract_inverted_index":{"Deciding":[0],"3-colorability":[1],"for":[2,14,40],"general":[3],"plane":[4],"graphs":[5],"is":[6],"known":[7],"to":[8,53,67,97],"be":[9,88],"an":[10],"NP-complete":[11],"problem.":[12],"However,":[13],"certain":[15],"families":[16],"of":[17,29,35,100],"graphs,":[18],"like":[19],"triangulations,":[20,36],"polynomial":[21],"time":[22],"algorithms":[23],"exist.":[24],"We":[25],"consider":[26,57],"the":[27,98],"family":[28],"pseudo-triangulations,":[30],"which":[31],"are":[32,81,102],"a":[33],"generalization":[34],"and":[37],"prove":[38],"NP-completeness":[39],"this":[41],"class.":[42],"This":[43],"result":[44],"also":[45,103],"holds":[46],"if":[47],"we":[48,71],"bound":[49],"their":[50],"face":[51,62,78],"degree":[52,63,79],"four,":[54],"or":[55],"exclusively":[56],"pointed":[58,74],"pseudo-triangulations":[59,75,101],"with":[60,76],"maximum":[61,77],"five.":[64],"In":[65],"contrast":[66],"these":[68],"completeness":[69],"results,":[70],"show":[72],"that":[73],"four":[80],"always":[82],"3-colorable.":[83],"An":[84],"according":[85],"3-coloring":[86],"can":[87],"found":[89],"in":[90],"linear":[91],"time.":[92],"Some":[93],"complexity":[94],"results":[95],"relating":[96],"rank":[99],"given.":[104]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}