{"id":"https://openalex.org/W1999344612","doi":"https://doi.org/10.1007/s00493-008-2385-y","title":"A colorful theorem on transversal lines to plane convex sets","display_name":"A colorful theorem on transversal lines to plane convex sets","publication_year":2008,"publication_date":"2008-07-01","ids":{"openalex":"https://openalex.org/W1999344612","doi":"https://doi.org/10.1007/s00493-008-2385-y","mag":"1999344612"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-008-2385-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-008-2385-y","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":"Combinatorica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090297714","display_name":"Jorge L. Arocha","orcid":"https://orcid.org/0000-0003-4050-9082"},"institutions":[{"id":"https://openalex.org/I167724894","display_name":"Universidad Aut\u00f3noma de la Ciudad de M\u00e9xico","ror":"https://ror.org/04q0r6m34","country_code":"MX","type":"education","lineage":["https://openalex.org/I167724894"]},{"id":"https://openalex.org/I8961855","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25","country_code":"MX","type":"education","lineage":["https://openalex.org/I8961855"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Jorge L. Arocha","raw_affiliation_strings":["Instituto de Matem\u00e1ticas, Universidad Nacional Aut\u00f3noma de M\u00e9xico Ciudad Universitaria, M\u00e9xico D.F., 04510, Mexico","Universidad Nacional Aut\u00f3noma de M\u00e9xico Ciudad Universitaria, Instituto de Matem\u00e1ticas, 04510, M\u00e9xico D.F., Mexico#TAB#"],"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1ticas, Universidad Nacional Aut\u00f3noma de M\u00e9xico Ciudad Universitaria, M\u00e9xico D.F., 04510, Mexico","institution_ids":["https://openalex.org/I167724894","https://openalex.org/I8961855"]},{"raw_affiliation_string":"Universidad Nacional Aut\u00f3noma de M\u00e9xico Ciudad Universitaria, Instituto de Matem\u00e1ticas, 04510, M\u00e9xico D.F., Mexico#TAB#","institution_ids":["https://openalex.org/I8961855"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079274572","display_name":"Javier Bracho","orcid":"https://orcid.org/0000-0003-4811-3760"},"institutions":[{"id":"https://openalex.org/I167724894","display_name":"Universidad Aut\u00f3noma de la Ciudad de M\u00e9xico","ror":"https://ror.org/04q0r6m34","country_code":"MX","type":"education","lineage":["https://openalex.org/I167724894"]},{"id":"https://openalex.org/I8961855","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25","country_code":"MX","type":"education","lineage":["https://openalex.org/I8961855"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Javier Bracho","raw_affiliation_strings":["Instituto de Matem\u00e1ticas, Universidad Nacional Aut\u00f3noma de M\u00e9xico Ciudad Universitaria, M\u00e9xico D.F., 04510, Mexico","Universidad Nacional Aut\u00f3noma de M\u00e9xico Ciudad Universitaria, Instituto de Matem\u00e1ticas, 04510, M\u00e9xico D.F., Mexico#TAB#"],"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1ticas, Universidad Nacional Aut\u00f3noma de M\u00e9xico Ciudad Universitaria, M\u00e9xico D.F., 04510, Mexico","institution_ids":["https://openalex.org/I167724894","https://openalex.org/I8961855"]},{"raw_affiliation_string":"Universidad Nacional Aut\u00f3noma de M\u00e9xico Ciudad Universitaria, Instituto de Matem\u00e1ticas, 04510, M\u00e9xico D.F., Mexico#TAB#","institution_ids":["https://openalex.org/I8961855"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063551926","display_name":"Luis Montejano","orcid":"https://orcid.org/0000-0003-3101-6518"},"institutions":[{"id":"https://openalex.org/I8961855","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25","country_code":"MX","type":"education","lineage":["https://openalex.org/I8961855"]},{"id":"https://openalex.org/I167724894","display_name":"Universidad Aut\u00f3noma de la Ciudad de M\u00e9xico","ror":"https://ror.org/04q0r6m34","country_code":"MX","type":"education","lineage":["https://openalex.org/I167724894"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Luis Montejano","raw_affiliation_strings":["Instituto de Matem\u00e1ticas, Universidad Nacional Aut\u00f3noma de M\u00e9xico Ciudad Universitaria, M\u00e9xico D.F., 04510, Mexico","Universidad Nacional Aut\u00f3noma de M\u00e9xico Ciudad Universitaria, Instituto de Matem\u00e1ticas, 04510, M\u00e9xico D.F., Mexico#TAB#"],"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1ticas, Universidad Nacional Aut\u00f3noma de M\u00e9xico Ciudad Universitaria, M\u00e9xico D.F., 04510, Mexico","institution_ids":["https://openalex.org/I167724894","https://openalex.org/I8961855"]},{"raw_affiliation_string":"Universidad Nacional Aut\u00f3noma de M\u00e9xico Ciudad Universitaria, Instituto de Matem\u00e1ticas, 04510, M\u00e9xico D.F., Mexico#TAB#","institution_ids":["https://openalex.org/I8961855"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5090297714"],"corresponding_institution_ids":["https://openalex.org/I167724894","https://openalex.org/I8961855"],"apc_list":null,"apc_paid":null,"fwci":0.7438,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.81264223,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"28","issue":"4","first_page":"379","last_page":"384"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9983000159263611,"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":0.9983000159263611,"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":0.9958999752998352,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9957000017166138,"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/transversal","display_name":"Transversal (combinatorics)","score":0.9389177560806274},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7930587530136108},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5825993418693542},{"id":"https://openalex.org/keywords/colored","display_name":"Colored","score":0.5651916265487671},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5560330748558044},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5517890453338623},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.5168931484222412},{"id":"https://openalex.org/keywords/krein\u2013milman-theorem","display_name":"Krein\u2013Milman theorem","score":0.4177425503730774},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.3096078634262085},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1822684109210968},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1219433844089508},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.07156863808631897},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.04507976770401001}],"concepts":[{"id":"https://openalex.org/C2780130068","wikidata":"https://www.wikidata.org/wiki/Q2208651","display_name":"Transversal (combinatorics)","level":2,"score":0.9389177560806274},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7930587530136108},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5825993418693542},{"id":"https://openalex.org/C2778307483","wikidata":"https://www.wikidata.org/wiki/Q5149038","display_name":"Colored","level":2,"score":0.5651916265487671},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5560330748558044},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5517890453338623},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.5168931484222412},{"id":"https://openalex.org/C173688413","wikidata":"https://www.wikidata.org/wiki/Q642620","display_name":"Krein\u2013Milman theorem","level":5,"score":0.4177425503730774},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.3096078634262085},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1822684109210968},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1219433844089508},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.07156863808631897},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.04507976770401001},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00493-008-2385-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-008-2385-y","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":"Combinatorica","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.44999998807907104,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1970823736","https://openalex.org/W1984879308","https://openalex.org/W1994709142","https://openalex.org/W2004331157","https://openalex.org/W2025154610","https://openalex.org/W2053369489","https://openalex.org/W2070830450","https://openalex.org/W2213853570","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1592143084","https://openalex.org/W3557672","https://openalex.org/W4288324104","https://openalex.org/W2951573408","https://openalex.org/W4238664286","https://openalex.org/W2941078816","https://openalex.org/W1999344612","https://openalex.org/W2343476731","https://openalex.org/W1534302995","https://openalex.org/W72541825"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}