{"id":"https://openalex.org/W1984100933","doi":"https://doi.org/10.1017/s0963548306007711","title":"Strong Isometric Dimension, Biclique Coverings, and Sperner's Theorem","display_name":"Strong Isometric Dimension, Biclique Coverings, and Sperner's Theorem","publication_year":2006,"publication_date":"2006-08-14","ids":{"openalex":"https://openalex.org/W1984100933","doi":"https://doi.org/10.1017/s0963548306007711","mag":"1984100933"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548306007711","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548306007711","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://dk.um.si/IzpisGradiva.php?id=51594","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019723815","display_name":"Dalibor Fron\u010dek","orcid":"https://orcid.org/0000-0003-4528-2059"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]},{"id":"https://openalex.org/I4210115145","display_name":"University of Minnesota, Duluth","ror":"https://ror.org/01hy4qx27","country_code":"US","type":"education","lineage":["https://openalex.org/I4210115145"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"DALIBOR FRON\u010cEK","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Minnesota Duluth, 1117 University Drive, Duluth, MN 55812, USA (e-mail:","Department of Mathematics and Statistics, University of Minnesota Duluth, 1117 University Drive, Duluth, MN 55812, USA (e-mail: dfroncek@d.umn.edu)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Minnesota Duluth, 1117 University Drive, Duluth, MN 55812, USA (e-mail:","institution_ids":["https://openalex.org/I4210115145"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Minnesota Duluth, 1117 University Drive, Duluth, MN 55812, USA (e-mail: dfroncek@d.umn.edu)#TAB#","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091905694","display_name":"Janja Jerebic","orcid":"https://orcid.org/0000-0002-9600-9952"},"institutions":[{"id":"https://openalex.org/I37696226","display_name":"University of Maribor","ror":"https://ror.org/01d5jce07","country_code":"SI","type":"education","lineage":["https://openalex.org/I37696226"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"JANJA JEREBIC","raw_affiliation_strings":["Department of Mathematics and Computer Science, PeF, University of Maribor, Koro\u0161ska cesta 160, 2000 Maribor, Slovenia (e-mail:","Department of Mathematics and Computer Science, PeF, University of Maribor, Koro\u0161ska cesta 160, 2000 Maribor, Slovenia (e-mail: janja.jerebic@uni-mb.si, sandi.klavzar@uni-mb.si)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, PeF, University of Maribor, Koro\u0161ska cesta 160, 2000 Maribor, Slovenia (e-mail:","institution_ids":["https://openalex.org/I37696226"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, PeF, University of Maribor, Koro\u0161ska cesta 160, 2000 Maribor, Slovenia (e-mail: janja.jerebic@uni-mb.si, sandi.klavzar@uni-mb.si)#TAB#","institution_ids":["https://openalex.org/I37696226"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049148828","display_name":"Sandi Klav\u017ear","orcid":"https://orcid.org/0000-0002-1556-4744"},"institutions":[{"id":"https://openalex.org/I37696226","display_name":"University of Maribor","ror":"https://ror.org/01d5jce07","country_code":"SI","type":"education","lineage":["https://openalex.org/I37696226"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"SANDI KLAV\u017dAR","raw_affiliation_strings":["Department of Mathematics and Computer Science, PeF, University of Maribor, Koro\u0161ska cesta 160, 2000 Maribor, Slovenia (e-mail:","Department of Mathematics and Computer Science, PeF, University of Maribor, Koro\u0161ska cesta 160, 2000 Maribor, Slovenia (e-mail: janja.jerebic@uni-mb.si, sandi.klavzar@uni-mb.si)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, PeF, University of Maribor, Koro\u0161ska cesta 160, 2000 Maribor, Slovenia (e-mail:","institution_ids":["https://openalex.org/I37696226"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, PeF, University of Maribor, Koro\u0161ska cesta 160, 2000 Maribor, Slovenia (e-mail: janja.jerebic@uni-mb.si, sandi.klavzar@uni-mb.si)#TAB#","institution_ids":["https://openalex.org/I37696226"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091791372","display_name":"Petr Kov\u00e1\u0159","orcid":"https://orcid.org/0000-0002-7847-5060"},"institutions":[{"id":"https://openalex.org/I142208455","display_name":"VSB - Technical University of Ostrava","ror":"https://ror.org/05x8mcb75","country_code":"CZ","type":"education","lineage":["https://openalex.org/I142208455"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"PETR KOV\u00c1\u0158","raw_affiliation_strings":["Department of Mathematics and Descriptive Geometry, Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava-Poruba, Czech Republic (e-mail:","Department of Mathematics and Descriptive Geometry, Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava-Poruba, Czech Republic (e-mail: petr.kovar@vsb.cz)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Descriptive Geometry, Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava-Poruba, Czech Republic (e-mail:","institution_ids":["https://openalex.org/I142208455"]},{"raw_affiliation_string":"Department of Mathematics and Descriptive Geometry, Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava-Poruba, Czech Republic (e-mail: petr.kovar@vsb.cz)#TAB#","institution_ids":["https://openalex.org/I142208455"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0119,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.75453943,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"16","issue":"2","first_page":"271","last_page":"275"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9998000264167786,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9990000128746033,"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/T11476","display_name":"Graph theory and applications","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/isometric-exercise","display_name":"Isometric exercise","score":0.8702723383903503},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7333453893661499},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7007606029510498},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.666620135307312},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.526988685131073},{"id":"https://openalex.org/keywords/hamming-graph","display_name":"Hamming graph","score":0.46020999550819397},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.44235676527023315},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4384177029132843},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4340803325176239},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.4203411936759949},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41138312220573425},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09869754314422607},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08301162719726562},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.05063861608505249}],"concepts":[{"id":"https://openalex.org/C103486182","wikidata":"https://www.wikidata.org/wiki/Q1216236","display_name":"Isometric exercise","level":2,"score":0.8702723383903503},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7333453893661499},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7007606029510498},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.666620135307312},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.526988685131073},{"id":"https://openalex.org/C29696283","wikidata":"https://www.wikidata.org/wiki/Q369440","display_name":"Hamming graph","level":5,"score":0.46020999550819397},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.44235676527023315},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4384177029132843},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4340803325176239},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.4203411936759949},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41138312220573425},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09869754314422607},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08301162719726562},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.05063861608505249},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.0},{"id":"https://openalex.org/C42407357","wikidata":"https://www.wikidata.org/wiki/Q521","display_name":"Physiology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s0963548306007711","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548306007711","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:dk.um.si:IzpisGradiva.php?id=51594","is_oa":true,"landing_page_url":"https://dk.um.si/IzpisGradiva.php?id=51594","pdf_url":null,"source":{"id":"https://openalex.org/S4377196302","display_name":"University of Maribor digital library (University of Maribor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I37696226","host_organization_name":"University of Maribor","host_organization_lineage":["https://openalex.org/I37696226"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, probability &amp; computing, vol. 2, no. 16, pp. 271-275, 2007.","raw_type":"info:eu-repo/semantics/other"},{"id":"pmh:oai:dspace.vsb.cz:10084/59882","is_oa":false,"landing_page_url":"http://hdl.handle.net/10084/59882","pdf_url":null,"source":{"id":"https://openalex.org/S4306401668","display_name":"DSpace V\u0160B-TUO (V\u0160B-TUO)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142208455","host_organization_name":"VSB - Technical University of Ostrava","host_organization_lineage":["https://openalex.org/I142208455"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:dk.um.si:IzpisGradiva.php?id=51594","is_oa":true,"landing_page_url":"https://dk.um.si/IzpisGradiva.php?id=51594","pdf_url":null,"source":{"id":"https://openalex.org/S4377196302","display_name":"University of Maribor digital library (University of Maribor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I37696226","host_organization_name":"University of Maribor","host_organization_lineage":["https://openalex.org/I37696226"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, probability &amp; computing, vol. 2, no. 16, pp. 271-275, 2007.","raw_type":"info:eu-repo/semantics/other"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W71943752","https://openalex.org/W174718643","https://openalex.org/W1020681818","https://openalex.org/W1567844118","https://openalex.org/W1966820817","https://openalex.org/W1988483130","https://openalex.org/W1998167411","https://openalex.org/W2028400828","https://openalex.org/W2061396714","https://openalex.org/W2079325670","https://openalex.org/W2121281842","https://openalex.org/W2143965437","https://openalex.org/W2161431783","https://openalex.org/W2330548796","https://openalex.org/W2611185757","https://openalex.org/W2736254659","https://openalex.org/W6634175707","https://openalex.org/W6740985638"],"related_works":["https://openalex.org/W2091826982","https://openalex.org/W245205139","https://openalex.org/W2036057584","https://openalex.org/W2107875203","https://openalex.org/W4234658180","https://openalex.org/W4235849992","https://openalex.org/W4246000090","https://openalex.org/W2910933086","https://openalex.org/W3143578817","https://openalex.org/W4288630335"],"abstract_inverted_index":{"The":[0],"strong":[1,20,29],"isometric":[2,30],"dimension":[3,31],"of":[4,22,32],"a":[5],"graph":[6],"G":[7,15],"is":[8,41],"the":[9,19,28,33],"least":[10],"number":[11],"k":[12,23],"such":[13],"that":[14],"isometrically":[16],"embeds":[17],"into":[18],"product":[21],"paths.":[24],"Using":[25],"Sperner's":[26],"theorem,":[27],"Hamming":[34],"graphs":[35],"K":[36,39],"2":[37],"\u25a1":[38],"n":[40],"determined.":[42]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
