{"id":"https://openalex.org/W2046340748","doi":"https://doi.org/10.1007/pl00009343","title":"Intersection of Curves and Crossing Number of C m \u00d7 C n on Surfaces","display_name":"Intersection of Curves and Crossing Number of C m \u00d7 C n on Surfaces","publication_year":1998,"publication_date":"1998-02-01","ids":{"openalex":"https://openalex.org/W2046340748","doi":"https://doi.org/10.1007/pl00009343","mag":"2046340748"},"language":"en","primary_location":{"id":"doi:10.1007/pl00009343","is_oa":true,"landing_page_url":"https://doi.org/10.1007/pl00009343","pdf_url":"https://link.springer.com/content/pdf/10.1007/PL00009343.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/PL00009343.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113492014","display_name":"F. Shahrokhi","orcid":null},"institutions":[{"id":"https://openalex.org/I123534392","display_name":"University of North Texas","ror":"https://ror.org/00v97ad02","country_code":"US","type":"education","lineage":["https://openalex.org/I123534392"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"F. Shahrokhi","raw_affiliation_strings":["Department of Computer Science, University of North Texas, P.O.Box 13886, Denton, TX 76203-3886, USA, , , , , , US","Department of Computer Science, University of North Texas, P.O.Box 13886, Denton, TX 76203-3886, USA, , US"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of North Texas, P.O.Box 13886, Denton, TX 76203-3886, USA, , , , , , US","institution_ids":["https://openalex.org/I123534392"]},{"raw_affiliation_string":"Department of Computer Science, University of North Texas, P.O.Box 13886, Denton, TX 76203-3886, USA, , US","institution_ids":["https://openalex.org/I123534392"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073592264","display_name":"Ond\u0159ej S\u00fdkora","orcid":null},"institutions":[{"id":"https://openalex.org/I207624831","display_name":"Slovak Academy of Sciences","ror":"https://ror.org/03h7qq074","country_code":"SK","type":"funder","lineage":["https://openalex.org/I207624831"]}],"countries":["SK"],"is_corresponding":false,"raw_author_name":"O. S\u00fdkora","raw_affiliation_strings":["Institute for Informatics, Slovak Academy of Sciences, P.O.Box 56, 840 00 Bratislava, Slovak Republic, , , , , , SK","Institute for Informatics, Slovak Academy of Sciences, P.O.Box 56, 840 00 Bratislava, Slovak Republic, SK"],"affiliations":[{"raw_affiliation_string":"Institute for Informatics, Slovak Academy of Sciences, P.O.Box 56, 840 00 Bratislava, Slovak Republic, , , , , , SK","institution_ids":["https://openalex.org/I207624831"]},{"raw_affiliation_string":"Institute for Informatics, Slovak Academy of Sciences, P.O.Box 56, 840 00 Bratislava, Slovak Republic, SK","institution_ids":["https://openalex.org/I207624831"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021815150","display_name":"L. A. Sz\u00e9kely","orcid":null},"institutions":[{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"L. A. Sz\u00e9kely","raw_affiliation_strings":["Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA, , , , , , US","Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA, , US"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA, , , , , , US","institution_ids":["https://openalex.org/I155781252"]},{"raw_affiliation_string":"Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA, , US","institution_ids":["https://openalex.org/I155781252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063290861","display_name":"Imrich Vrt\u2019o","orcid":null},"institutions":[{"id":"https://openalex.org/I207624831","display_name":"Slovak Academy of Sciences","ror":"https://ror.org/03h7qq074","country_code":"SK","type":"funder","lineage":["https://openalex.org/I207624831"]}],"countries":["SK"],"is_corresponding":false,"raw_author_name":"I. Vrt'o","raw_affiliation_strings":["Institute for Informatics, Slovak Academy of Sciences, P.O.Box 56, 840 00 Bratislava, Slovak Republic, , , , , , SK","Institute for Informatics, Slovak Academy of Sciences, P.O.Box 56, 840 00 Bratislava, Slovak Republic, SK"],"affiliations":[{"raw_affiliation_string":"Institute for Informatics, Slovak Academy of Sciences, P.O.Box 56, 840 00 Bratislava, Slovak Republic, , , , , , SK","institution_ids":["https://openalex.org/I207624831"]},{"raw_affiliation_string":"Institute for Informatics, Slovak Academy of Sciences, P.O.Box 56, 840 00 Bratislava, Slovak Republic, SK","institution_ids":["https://openalex.org/I207624831"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5113492014"],"corresponding_institution_ids":["https://openalex.org/I123534392"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.8572,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.86159844,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"19","issue":"2","first_page":"237","last_page":"247"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9995999932289124,"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":0.9995999932289124,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9836999773979187,"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/mathematics","display_name":"Mathematics","score":0.8199490904808044},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7313982248306274},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.6085456609725952},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5993821024894714},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.5505061149597168},{"id":"https://openalex.org/keywords/plane-curve","display_name":"Plane curve","score":0.5049777626991272},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.4885922074317932},{"id":"https://openalex.org/keywords/projective-plane","display_name":"Projective plane","score":0.4628075957298279},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4591521620750427},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.41154593229293823},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2876247763633728}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8199490904808044},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7313982248306274},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6085456609725952},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5993821024894714},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.5505061149597168},{"id":"https://openalex.org/C43809302","wikidata":"https://www.wikidata.org/wiki/Q1060874","display_name":"Plane curve","level":2,"score":0.5049777626991272},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.4885922074317932},{"id":"https://openalex.org/C39290043","wikidata":"https://www.wikidata.org/wiki/Q1475760","display_name":"Projective plane","level":3,"score":0.4628075957298279},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4591521620750427},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.41154593229293823},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2876247763633728},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/pl00009343","is_oa":true,"landing_page_url":"https://doi.org/10.1007/pl00009343","pdf_url":"https://link.springer.com/content/pdf/10.1007/PL00009343.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"}],"best_oa_location":{"id":"doi:10.1007/pl00009343","is_oa":true,"landing_page_url":"https://doi.org/10.1007/pl00009343","pdf_url":"https://link.springer.com/content/pdf/10.1007/PL00009343.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/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G973945576","display_name":"Crossing Number Problems in Geometric Drawings of Graphs","funder_award_id":"9528228","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320312330","display_name":"Slovensk\u00e1 Akad\u00e9mia Vied","ror":"https://ror.org/03h7qq074"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2046340748.pdf","grobid_xml":"https://content.openalex.org/works/W2046340748.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W86126052","https://openalex.org/W636131375","https://openalex.org/W1415354223","https://openalex.org/W1516470529","https://openalex.org/W1558273801","https://openalex.org/W1579439722","https://openalex.org/W1977621057","https://openalex.org/W1995518672","https://openalex.org/W2015661373","https://openalex.org/W2032958186","https://openalex.org/W2076984436","https://openalex.org/W2115843823","https://openalex.org/W2146643158","https://openalex.org/W2212201998","https://openalex.org/W3145896515"],"related_works":["https://openalex.org/W2952362912","https://openalex.org/W4300892262","https://openalex.org/W2070190818","https://openalex.org/W2597073605","https://openalex.org/W2962748612","https://openalex.org/W2767850798","https://openalex.org/W3042196055","https://openalex.org/W2140952994","https://openalex.org/W2359442960","https://openalex.org/W4212787620"],"abstract_inverted_index":null,"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}