{"id":"https://openalex.org/W2614087704","doi":"https://doi.org/10.1007/978-3-540-77537-9_4","title":"A Bipartite Strengthening of the Crossing Lemma","display_name":"A Bipartite Strengthening of the Crossing Lemma","publication_year":2008,"publication_date":"2008-01-30","ids":{"openalex":"https://openalex.org/W2614087704","doi":"https://doi.org/10.1007/978-3-540-77537-9_4","mag":"2614087704"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-77537-9_4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-540-77537-9_4","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-540-77537-9_4.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/10.1007/978-3-540-77537-9_4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112361944","display_name":"Jacob Fox","orcid":"https://orcid.org/0000-0002-0664-497X"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jacob Fox","raw_affiliation_strings":["Department of Mathematics, Princeton University, Princeton, NJ, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032398271","display_name":"J\u00e1nos Pach","orcid":"https://orcid.org/0000-0002-2389-2035"},"institutions":[{"id":"https://openalex.org/I125687163","display_name":"City College of New York","ror":"https://ror.org/00wmhkr98","country_code":"US","type":"education","lineage":["https://openalex.org/I125687163"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J\u00e1nos Pach","raw_affiliation_strings":["City College, CUNY and Courant Institute, NYU, New York, NY, USA"],"affiliations":[{"raw_affiliation_string":"City College, CUNY and Courant Institute, NYU, New York, NY, USA","institution_ids":["https://openalex.org/I125687163"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030799674","display_name":"Csaba D. T\u00f3th","orcid":"https://orcid.org/0000-0002-8769-3190"},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Csaba D. T\u00f3th","raw_affiliation_strings":["University of Calgary, Calgary, AB, Canada"],"affiliations":[{"raw_affiliation_string":"University of Calgary, Calgary, AB, Canada","institution_ids":["https://openalex.org/I168635309"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5112361944"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.5919,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.6958042,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"13","last_page":"24"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9853000044822693,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9632999897003174,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"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/combinatorics","display_name":"Combinatorics","score":0.8866788148880005},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7562299370765686},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.7193156480789185},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.6425360441207886},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.566102147102356},{"id":"https://openalex.org/keywords/crossing-number","display_name":"Crossing number (knot theory)","score":0.5582578182220459},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.5439825057983398},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5277089476585388},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5007431507110596},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3590717613697052},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14947888255119324}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8866788148880005},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7562299370765686},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.7193156480789185},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6425360441207886},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.566102147102356},{"id":"https://openalex.org/C2777724877","wikidata":"https://www.wikidata.org/wiki/Q2548661","display_name":"Crossing number (knot theory)","level":3,"score":0.5582578182220459},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.5439825057983398},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5277089476585388},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5007431507110596},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3590717613697052},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14947888255119324},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/978-3-540-77537-9_4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-540-77537-9_4","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-540-77537-9_4.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:824","is_oa":false,"landing_page_url":"http://gdea.informatik.uni-koeln.de/824/","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:infoscience.tind.io:129375","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/129375","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"","raw_type":"book part or chapter"}],"best_oa_location":{"id":"doi:10.1007/978-3-540-77537-9_4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-540-77537-9_4","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-540-77537-9_4.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":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309102","display_name":"City University of New York","ror":"https://ror.org/00453a208"},{"id":"https://openalex.org/F4320321994","display_name":"Hungarian Scientific Research Fund","ror":"https://ror.org/00v349e63"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2614087704.pdf","grobid_xml":"https://content.openalex.org/works/W2614087704.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W13988344","https://openalex.org/W200206406","https://openalex.org/W1577934253","https://openalex.org/W1595497480","https://openalex.org/W1992365801","https://openalex.org/W1993083969","https://openalex.org/W1998666916","https://openalex.org/W2000052110","https://openalex.org/W2003689202","https://openalex.org/W2024937369","https://openalex.org/W2038643780","https://openalex.org/W2039857505","https://openalex.org/W2053910492","https://openalex.org/W2060438030","https://openalex.org/W2066782398","https://openalex.org/W2074825559","https://openalex.org/W2101764588","https://openalex.org/W2136361847","https://openalex.org/W2144898438","https://openalex.org/W2146689185","https://openalex.org/W2149757010","https://openalex.org/W2155681397","https://openalex.org/W2166961358","https://openalex.org/W2168138462","https://openalex.org/W2319149236","https://openalex.org/W2912209775","https://openalex.org/W4211205179","https://openalex.org/W4235946010","https://openalex.org/W4247006625"],"related_works":["https://openalex.org/W2174899211","https://openalex.org/W2091826982","https://openalex.org/W4400909662","https://openalex.org/W2921162226","https://openalex.org/W2036057584","https://openalex.org/W3022526073","https://openalex.org/W4246000090","https://openalex.org/W2107875203","https://openalex.org/W4234658180","https://openalex.org/W3098480989"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2017-05-19T00:00:00"}