{"id":"https://openalex.org/W1929742047","doi":"https://doi.org/10.1007/3-540-45848-4_8","title":"An Improved Lower Bound for Crossing Numbers","display_name":"An Improved Lower Bound for Crossing Numbers","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1929742047","doi":"https://doi.org/10.1007/3-540-45848-4_8","mag":"1929742047"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-45848-4_8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/3-540-45848-4_8","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F3-540-45848-4_8.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007%2F3-540-45848-4_8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057625550","display_name":"Hristo Djidjev","orcid":"https://orcid.org/0000-0001-9286-8824"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Hristo Djidjev","raw_affiliation_strings":["Department of Computer Science, Warwick University, CV4 7AL, Coventry, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Warwick University, CV4 7AL, Coventry, UK","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063290861","display_name":"Imrich Vrt\u2019o","orcid":null},"institutions":[{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]},{"id":"https://openalex.org/I4210105926","display_name":"Institute of Mathematics and Informatics","ror":"https://ror.org/01b5dy719","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]}],"countries":["BG","CZ"],"is_corresponding":false,"raw_author_name":"Imrich Vrt\u2019o","raw_affiliation_strings":["Department of Informatics, Institute of Mathematics, D\u00fabravsk\u00e1 9, 842 35, Bratislava, Slovak Republic"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, Institute of Mathematics, D\u00fabravsk\u00e1 9, 842 35, Bratislava, Slovak Republic","institution_ids":["https://openalex.org/I4210105926","https://openalex.org/I4210120266"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057625550"],"corresponding_institution_ids":["https://openalex.org/I39555362"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.7633,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.66386555,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"96","last_page":"101"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9821000099182129,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9751999974250793,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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":0.8386783599853516},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6907534599304199},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6448200941085815},{"id":"https://openalex.org/keywords/crossing-number","display_name":"Crossing number (knot theory)","score":0.6234437823295593},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6140066385269165},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5566076636314392},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5522206425666809},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.4919123649597168},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.47437506914138794},{"id":"https://openalex.org/keywords/bisection","display_name":"Bisection","score":0.44388195872306824},{"id":"https://openalex.org/keywords/bound-graph","display_name":"Bound graph","score":0.4158173203468323},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34257328510284424},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23698687553405762},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.15180760622024536},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1238945722579956},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.11217600107192993},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05443495512008667},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.048386722803115845}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8386783599853516},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6907534599304199},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6448200941085815},{"id":"https://openalex.org/C2777724877","wikidata":"https://www.wikidata.org/wiki/Q2548661","display_name":"Crossing number (knot theory)","level":3,"score":0.6234437823295593},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6140066385269165},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5566076636314392},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5522206425666809},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.4919123649597168},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.47437506914138794},{"id":"https://openalex.org/C31599958","wikidata":"https://www.wikidata.org/wiki/Q3128632","display_name":"Bisection","level":2,"score":0.44388195872306824},{"id":"https://openalex.org/C121134508","wikidata":"https://www.wikidata.org/wiki/Q4949882","display_name":"Bound graph","level":5,"score":0.4158173203468323},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34257328510284424},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23698687553405762},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.15180760622024536},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1238945722579956},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.11217600107192993},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05443495512008667},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.048386722803115845},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/3-540-45848-4_8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/3-540-45848-4_8","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F3-540-45848-4_8.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:gdea.informatik.uni-koeln.de:423","is_oa":false,"landing_page_url":"http://gdea.informatik.uni-koeln.de/423/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196197","display_name":"gdea - Graph Drawing E-print Archive (GDEA)","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference Paper"},{"id":"pmh:oai:publications.rwth-aachen.de:112724","is_oa":false,"landing_page_url":"https://publications.rwth-aachen.de/record/112724","pdf_url":null,"source":{"id":"https://openalex.org/S4306401362","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Graph drawing : 9th international symposium ; revised papers / GD 2001, Vienna, Austria, September 23 - 26, 2001. Petra Mutzel ... (ed.)<br/>Graph drawing : 9. international symposium, GD 2001, Vienna, Austria, 2001-09-23 - 2001-09-26","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1007/3-540-45848-4_8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/3-540-45848-4_8","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F3-540-45848-4_8.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5398132153","display_name":null,"funder_award_id":"DFG grant","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320323641","display_name":"Vedeck\u00e1 Grantov\u00e1 Agent\u00fara M\u0160VVa\u0160 SR a SAV","ror":"https://ror.org/044gwpv05"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1929742047.pdf","grobid_xml":"https://content.openalex.org/works/W1929742047.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W4007448","https://openalex.org/W86126052","https://openalex.org/W1507349209","https://openalex.org/W1521554751","https://openalex.org/W1595497480","https://openalex.org/W1971417331","https://openalex.org/W1983901430","https://openalex.org/W1998306675","https://openalex.org/W2008555705","https://openalex.org/W2024534209","https://openalex.org/W2024937369","https://openalex.org/W2052867211","https://openalex.org/W2060538865","https://openalex.org/W2083578892","https://openalex.org/W2102664288","https://openalex.org/W2111635834","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3033929256","https://openalex.org/W3011774801","https://openalex.org/W2937406279","https://openalex.org/W4381094520","https://openalex.org/W2809930434","https://openalex.org/W3159927204","https://openalex.org/W1577934253","https://openalex.org/W2024800008","https://openalex.org/W2793144387","https://openalex.org/W2157163513"],"abstract_inverted_index":null,"counts_by_year":[{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
