{"id":"https://openalex.org/W3163375977","doi":"https://doi.org/10.1017/s0963548321000171","title":"Tur\u00e1n-type results for intersection graphs of boxes","display_name":"Tur\u00e1n-type results for intersection graphs of boxes","publication_year":2021,"publication_date":"2021-05-19","ids":{"openalex":"https://openalex.org/W3163375977","doi":"https://doi.org/10.1017/s0963548321000171","mag":"3163375977"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548321000171","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548321000171","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/F2BC191D56DC97328ECA7E7785960DEA/S0963548321000171a.pdf/div-class-title-turan-type-results-for-intersection-graphs-of-boxes-div.pdf","source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/F2BC191D56DC97328ECA7E7785960DEA/S0963548321000171a.pdf/div-class-title-turan-type-results-for-intersection-graphs-of-boxes-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040332950","display_name":"Istv\u00e1n Tomon","orcid":"https://orcid.org/0000-0001-8344-3592"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Istv\u00e1n Tomon","raw_affiliation_strings":["ETH Zurich, Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091745418","display_name":"Dmitriy Zakharov","orcid":"https://orcid.org/0000-0002-1570-548X"},"institutions":[{"id":"https://openalex.org/I118501908","display_name":"National Research University Higher School of Economics","ror":"https://ror.org/055f7t516","country_code":"RU","type":"education","lineage":["https://openalex.org/I118501908"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Dmitriy Zakharov","raw_affiliation_strings":["HSEMoscow, Russia","MIPTMoscow, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"HSEMoscow, Russia","institution_ids":["https://openalex.org/I118501908"]},{"raw_affiliation_string":"MIPTMoscow, Russia","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5040332950"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":2.3771,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.91682584,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"30","issue":"6","first_page":"982","last_page":"987"},"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":0.9994999766349792,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8545883893966675},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7529990077018738},{"id":"https://openalex.org/keywords/intersection-graph","display_name":"Intersection graph","score":0.7503350973129272},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6913203001022339},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6378548741340637},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5927499532699585},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5578159093856812},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.427179217338562},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4270193874835968},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4193892478942871},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.4161064624786377},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.1218981146812439},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07188805937767029}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8545883893966675},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7529990077018738},{"id":"https://openalex.org/C54540088","wikidata":"https://www.wikidata.org/wiki/Q3498041","display_name":"Intersection graph","level":4,"score":0.7503350973129272},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6913203001022339},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6378548741340637},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5927499532699585},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5578159093856812},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.427179217338562},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4270193874835968},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4193892478942871},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.4161064624786377},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.1218981146812439},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07188805937767029},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s0963548321000171","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548321000171","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/F2BC191D56DC97328ECA7E7785960DEA/S0963548321000171a.pdf/div-class-title-turan-type-results-for-intersection-graphs-of-boxes-div.pdf","source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/492180","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/492180","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Combinatorics, Probability & Computing, 30 (6)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"doi:10.3929/ethz-b-000492180","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000492180","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","issn_l":null,"issn":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1017/s0963548321000171","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548321000171","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/F2BC191D56DC97328ECA7E7785960DEA/S0963548321000171a.pdf/div-class-title-turan-type-results-for-intersection-graphs-of-boxes-div.pdf","source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4907092097","display_name":null,"funder_award_id":"075-15-2019-1926","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G7165436123","display_name":null,"funder_award_id":"200021_196965","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320330091","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3163375977.pdf","grobid_xml":"https://content.openalex.org/works/W3163375977.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1956452579","https://openalex.org/W2034834286","https://openalex.org/W2166961358","https://openalex.org/W2783200209","https://openalex.org/W2789327690","https://openalex.org/W2963208722","https://openalex.org/W3083477460","https://openalex.org/W3104752240","https://openalex.org/W3108948946","https://openalex.org/W3178431135","https://openalex.org/W3198368056"],"related_works":["https://openalex.org/W2106070061","https://openalex.org/W4390961156","https://openalex.org/W1963087247","https://openalex.org/W4312224320","https://openalex.org/W2371953206","https://openalex.org/W71032323","https://openalex.org/W2357388067","https://openalex.org/W3037552220","https://openalex.org/W1893408579","https://openalex.org/W2134071260"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,82],"short":[3],"note,":[4],"we":[5,84],"prove":[6],"the":[7,11,22,108],"following":[8],"analog":[9],"of":[10,17,25,37,90,97,103,117,130,137],"K\u0151v\u00e1ri\u2013S\u00f3s\u2013Tur\u00e1n":[12],"theorem":[13],"for":[14],"intersection":[15,23],"graphs":[16,102,129],"boxes.":[18],"If":[19],"G":[20,33,42],"is":[21,69],"graph":[24],"n":[26,49],"axis-parallel":[27],"boxes":[28],"in":[29,107],"$${{\\mathbb{R}}^d}$$":[30],"such":[31],"that":[32,87,126],"contains":[34],"no":[35],"copy":[36],"K":[38,98],"t,t":[39],",":[40],"then":[41],"has":[43],"at":[44],"most":[45],"ctn":[46],"(":[47,59],"log":[48],")":[50],"2":[51],"d":[52,60,65],"+3":[53],"edges,":[54],"where":[55],"c":[56,58],"=":[57],")>0":[61],"only":[62],"depends":[63],"on":[64,71],".":[66],"Our":[67],"proof":[68],"based":[70],"exploring":[72],"connections":[73],"between":[74],"boxicity,":[75],"separation":[76,131],"dimension":[77,132],"and":[78,95,105,122],"poset":[79],"dimension.":[80],"Using":[81],"approach,":[83],"also":[85],"show":[86,125],"a":[88,115],"construction":[89],"Basit,":[91],"Chernikov,":[92],"Starchenko,":[93],"Tao":[94],"Tran":[96],"2,2":[99],"-free":[100],"incidence":[101],"points":[104],"rectangles":[106],"plane":[109],"can":[110],"be":[111],"used":[112],"to":[113],"disprove":[114],"conjecture":[116],"Alon,":[118],"Basavaraju,":[119],"Chandran,":[120],"Mathew":[121],"Rajendraprasad.":[123],"We":[124],"there":[127],"exist":[128],"4":[133],"having":[134],"superlinear":[135],"number":[136],"edges.":[138]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}