{"id":"https://openalex.org/W1983707449","doi":"https://doi.org/10.1017/s0963548302005333","title":"Triangle-Freeness is Hard to Detect","display_name":"Triangle-Freeness is Hard to Detect","publication_year":2002,"publication_date":"2002-11-01","ids":{"openalex":"https://openalex.org/W1983707449","doi":"https://doi.org/10.1017/s0963548302005333","mag":"1983707449"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548302005333","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548302005333","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048543827","display_name":"Stasys Jukna","orcid":"https://orcid.org/0000-0002-2786-9326"},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]},{"id":"https://openalex.org/I74750888","display_name":"Lithuanian Academy of Sciences","ror":"https://ror.org/035gfy236","country_code":"LT","type":"other","lineage":["https://openalex.org/I74750888"]}],"countries":["DE","LT"],"is_corresponding":false,"raw_author_name":"S. JUKNA","raw_affiliation_strings":["Institute of Mathematics and Informatics, Akademijos 4, LT-2600 Vilnius, Lithuania","Universit\u00e4t Frankfurt, Institut f\u00fcr Informatik, Robert-Mayer-Strasse 11-15, D-60054 Frankfurt, Germany (e-mail:","Universit\u00e4t Frankfurt, Institut f\u00fcr Informatik, Robert-Mayer-Strasse 11-15, D-60054 Frankfurt, Germany (e-mail: jukna@thi.informatik.uni-frankfurt.de) and Institute of Mathematics and In ...#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Informatics, Akademijos 4, LT-2600 Vilnius, Lithuania","institution_ids":["https://openalex.org/I74750888"]},{"raw_affiliation_string":"Universit\u00e4t Frankfurt, Institut f\u00fcr Informatik, Robert-Mayer-Strasse 11-15, D-60054 Frankfurt, Germany (e-mail:","institution_ids":["https://openalex.org/I114090438"]},{"raw_affiliation_string":"Universit\u00e4t Frankfurt, Institut f\u00fcr Informatik, Robert-Mayer-Strasse 11-15, D-60054 Frankfurt, Germany (e-mail: jukna@thi.informatik.uni-frankfurt.de) and Institute of Mathematics and In ...#TAB#","institution_ids":["https://openalex.org/I114090438"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025007932","display_name":"Georg Schnitger","orcid":null},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"G. SCHNITGER","raw_affiliation_strings":["Universit\u00e4t Frankfurt, Institut f\u00fcr Informatik, Robert-Mayer-Strasse 11-15, D-60054 Frankfurt, Germany (e-mail:","Universit\u00e4t Frankfurt, Institut f\u00fcr Informatik, Robert-Mayer-Strasse 11-15, D-60054 Frankfurt, Germany (e-mail: jukna@thi.informatik.uni-frankfurt.de)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Frankfurt, Institut f\u00fcr Informatik, Robert-Mayer-Strasse 11-15, D-60054 Frankfurt, Germany (e-mail:","institution_ids":["https://openalex.org/I114090438"]},{"raw_affiliation_string":"Universit\u00e4t Frankfurt, Institut f\u00fcr Informatik, Robert-Mayer-Strasse 11-15, D-60054 Frankfurt, Germany (e-mail: jukna@thi.informatik.uni-frankfurt.de)#TAB#","institution_ids":["https://openalex.org/I114090438"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":1.173,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.76863594,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"11","issue":"6","first_page":"549","last_page":"569"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9994000196456909,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9994000196456909,"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/T11567","display_name":"semigroups and automata theory","score":0.9991000294685364,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/lemma","display_name":"Lemma (botany)","score":0.7950400114059448},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7589277029037476},{"id":"https://openalex.org/keywords/nondeterministic-algorithm","display_name":"Nondeterministic algorithm","score":0.6387023329734802},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5766276717185974},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.556221604347229},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5139884352684021},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4859553575515747},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.45556119084358215},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37936514616012573}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.7950400114059448},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7589277029037476},{"id":"https://openalex.org/C176181172","wikidata":"https://www.wikidata.org/wiki/Q3490301","display_name":"Nondeterministic algorithm","level":2,"score":0.6387023329734802},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5766276717185974},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.556221604347229},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5139884352684021},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4859553575515747},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45556119084358215},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37936514616012573},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548302005333","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548302005333","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1513200808","https://openalex.org/W1882041575","https://openalex.org/W2001736707","https://openalex.org/W2035763891","https://openalex.org/W2036586001","https://openalex.org/W2070913436","https://openalex.org/W2095012419","https://openalex.org/W2099986052","https://openalex.org/W2146207150","https://openalex.org/W2296545821","https://openalex.org/W2340787257"],"related_works":["https://openalex.org/W3006682748","https://openalex.org/W1097487277","https://openalex.org/W184826316","https://openalex.org/W3132573772","https://openalex.org/W2768610039","https://openalex.org/W1576777252","https://openalex.org/W4308265086","https://openalex.org/W2949964783","https://openalex.org/W4301452142","https://openalex.org/W2581389238"],"abstract_inverted_index":{"We":[0,86],"show":[1],"that":[2,47,74],"recognizing":[3],"the":[4,54,57],"K3-freeness":[5],"and":[6,22,43,94],"K4-freeness":[7],"of":[8,36,53,56,65,69],"graphs":[9],"is":[10,33,62,71],"hard,":[11],"respectively,":[12],"for":[13,23,48],"two-player":[14],"nondeterministic":[15,24],"communication":[16],"protocols":[17],"using":[18],"exponentially":[19,91],"many":[20,92],"partitions":[21],"syntactic":[25],"read-r":[26],"times":[27],"branching":[28],"programs.":[29],"The":[30],"key":[31],"ingredient":[32],"a":[34,37,63],"generalization":[35],"colouring":[38,52],"lemma,":[39],"due":[40],"to":[41,90,95],"Papadimitriou":[42],"Sipser,":[44],"which":[45,70],"says":[46],"every":[49],"balanced":[50],"red\u2014blue":[51],"edges":[55,82],"complete":[58],"n-vertex":[59],"graph":[60],"there":[61],"set":[64],"\u03b5n2":[66],"triangles,":[67],"none":[68],"monochromatic,":[72],"such":[73],"no":[75],"triangle":[76],"can":[77],"be":[78],"formed":[79],"by":[80],"picking":[81],"from":[83],"different":[84],"triangles.":[85],"extend":[87],"this":[88],"lemma":[89],"colourings":[93],"partial":[96],"colourings.":[97]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}