{"id":"https://openalex.org/W7128607495","doi":"https://doi.org/10.48550/arxiv.2602.09978","title":"The Parameterized Complexity of Geometric 1-Planarity","display_name":"The Parameterized Complexity of Geometric 1-Planarity","publication_year":2026,"publication_date":"2026-02-10","ids":{"openalex":"https://openalex.org/W7128607495","doi":"https://doi.org/10.48550/arxiv.2602.09978"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.09978","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125679125","display_name":"Alexander Firbas","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Firbas, Alexander","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5125679125"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.7152000069618225,"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":0.7152000069618225,"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":0.20649999380111694,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.014499999582767487,"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/kernelization","display_name":"Kernelization","score":0.9298999905586243},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.8439000248908997},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7045000195503235},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.492900013923645},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4498000144958496},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.39559999108314514},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.38850000500679016},{"id":"https://openalex.org/keywords/vertex-cover","display_name":"Vertex cover","score":0.382099986076355}],"concepts":[{"id":"https://openalex.org/C207225210","wikidata":"https://www.wikidata.org/wiki/Q1759539","display_name":"Kernelization","level":3,"score":0.9298999905586243},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.8439000248908997},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7045000195503235},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6459000110626221},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.492900013923645},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4925000071525574},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4498000144958496},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4311999976634979},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.39559999108314514},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.38850000500679016},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.382099986076355},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3741999864578247},{"id":"https://openalex.org/C136520226","wikidata":"https://www.wikidata.org/wiki/Q302814","display_name":"Geometric data analysis","level":2,"score":0.35109999775886536},{"id":"https://openalex.org/C7305733","wikidata":"https://www.wikidata.org/wiki/Q207961","display_name":"Geometric shape","level":2,"score":0.337799996137619},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.3098999857902527},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.27720001339912415},{"id":"https://openalex.org/C104065381","wikidata":"https://www.wikidata.org/wiki/Q1002535","display_name":"Geometric modeling","level":2,"score":0.27000001072883606},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C7605037","wikidata":"https://www.wikidata.org/wiki/Q327164","display_name":"Geometric probability","level":2,"score":0.2619999945163727}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.09978","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.09978","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.09978","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"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.09978","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0],"graph":[1],"is":[2,14,60],"geometric":[3,31],"1-planar":[4,32,49],"if":[5],"it":[6],"admits":[7],"a":[8,37,70,83,114,122],"straight-line":[9],"drawing":[10],"where":[11],"each":[12],"edge":[13,79],"crossed":[15],"at":[16],"most":[17],"once.":[18],"We":[19],"provide":[20,129],"the":[21,26,58,77,87,99,117],"first":[22],"systematic":[23],"study":[24],"of":[25,29,39,48,92,140],"parameterized":[27,64,75],"complexity":[28],"recognizing":[30],"graphs.":[33],"By":[34],"substantially":[35],"extending":[36],"technique":[38],"Bannister,":[40],"Cabello,":[41],"and":[42,96,147],"Eppstein,":[43],"combined":[44],"with":[45,121],"Thomassen's":[46],"characterization":[47],"embeddings":[50],"that":[51,57],"can":[52],"be":[53],"straightened,":[54],"we":[55,68,85,128],"show":[56],"problem":[59],"fixed-parameter":[61],"tractable":[62],"when":[63],"by":[65,76],"treedepth.":[66],"Furthermore,":[67],"obtain":[69],"kernel":[71,90],"for":[72,94,138],"Geometric":[73,111,133],"1-Planarity":[74,95,134],"feedback":[78,144],"number":[80],"$\\ell$.":[81],"As":[82],"by-product,":[84],"improve":[86],"best":[88],"known":[89],"size":[91],"$O((3\\ell)!)$":[93],"$k$-Planarity":[97],"under":[98,116],"same":[100,118],"parameterization":[101],"to":[102,110],"$O(\\ell":[103],"\\cdot":[104],"8^{\\ell})$.":[105],"Our":[106],"approach":[107],"naturally":[108],"extends":[109],"$k$-Planarity,":[112],"yielding":[113],"kernelization":[115],"parameterization,":[119],"albeit":[120],"larger":[123],"kernel.":[124],"Complementing":[125],"these":[126],"results,":[127],"matching":[130],"lower":[131],"bounds:":[132],"remains":[135],"\\NP-complete":[136],"even":[137],"graphs":[139],"bounded":[141,143,148],"pathwidth,":[142],"vertex":[145],"number,":[146],"bandwidth.":[149]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-02-12T00:00:00"}