{"id":"https://openalex.org/W2076599430","doi":"https://doi.org/10.1137/050633445","title":"Every Monotone Graph Property Is Testable","display_name":"Every Monotone Graph Property Is Testable","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2076599430","doi":"https://doi.org/10.1137/050633445","mag":"2076599430"},"language":"en","primary_location":{"id":"doi:10.1137/050633445","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050633445","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on 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/A5083469386","display_name":"Noga Alon","orcid":"https://orcid.org/0000-0003-1332-4883"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Noga Alon","raw_affiliation_strings":["[email\u00a0protected]#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[email\u00a0protected]#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089978763","display_name":"A. Shapira","orcid":"https://orcid.org/0000-0001-9902-0164"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Asaf Shapira","raw_affiliation_strings":["asafico@tau.ac.il#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"asafico@tau.ac.il#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.3872,"has_fulltext":false,"cited_by_count":72,"citation_normalized_percentile":{"value":0.9827675,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"38","issue":"2","first_page":"505","last_page":"522"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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":0.998199999332428,"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/T12288","display_name":"Optimization and Search Problems","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/graph-property","display_name":"Graph property","score":0.7444450855255127},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6921316981315613},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6387287378311157},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5939846634864807},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5585181713104248},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.5386097431182861},{"id":"https://openalex.org/keywords/complement-graph","display_name":"Complement graph","score":0.5081484317779541},{"id":"https://openalex.org/keywords/property-testing","display_name":"Property testing","score":0.5048204064369202},{"id":"https://openalex.org/keywords/null-graph","display_name":"Null graph","score":0.49971795082092285},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47108447551727295},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.45420122146606445},{"id":"https://openalex.org/keywords/critical-graph","display_name":"Critical graph","score":0.43685290217399597},{"id":"https://openalex.org/keywords/strength-of-a-graph","display_name":"Strength of a graph","score":0.41545575857162476}],"concepts":[{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.7444450855255127},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6921316981315613},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6387287378311157},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5939846634864807},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5585181713104248},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.5386097431182861},{"id":"https://openalex.org/C168291704","wikidata":"https://www.wikidata.org/wiki/Q902252","display_name":"Complement graph","level":5,"score":0.5081484317779541},{"id":"https://openalex.org/C123842658","wikidata":"https://www.wikidata.org/wiki/Q2918980","display_name":"Property testing","level":2,"score":0.5048204064369202},{"id":"https://openalex.org/C17169500","wikidata":"https://www.wikidata.org/wiki/Q3033506","display_name":"Null graph","level":5,"score":0.49971795082092285},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47108447551727295},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.45420122146606445},{"id":"https://openalex.org/C167750561","wikidata":"https://www.wikidata.org/wiki/Q1789512","display_name":"Critical graph","level":5,"score":0.43685290217399597},{"id":"https://openalex.org/C19332903","wikidata":"https://www.wikidata.org/wiki/Q7623247","display_name":"Strength of a graph","level":5,"score":0.41545575857162476},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050633445","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050633445","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1529556207","https://openalex.org/W1963993969","https://openalex.org/W1970630090","https://openalex.org/W1994434808","https://openalex.org/W2000079459","https://openalex.org/W2018925011","https://openalex.org/W2020551595","https://openalex.org/W2036501955","https://openalex.org/W2069816168","https://openalex.org/W2072808987","https://openalex.org/W2078289947","https://openalex.org/W2080767775","https://openalex.org/W2083580384","https://openalex.org/W2093276208","https://openalex.org/W2118212166","https://openalex.org/W2139374679","https://openalex.org/W2161620758","https://openalex.org/W2911327865","https://openalex.org/W3008660429","https://openalex.org/W3030488835"],"related_works":["https://openalex.org/W1968752573","https://openalex.org/W2171582965","https://openalex.org/W3091695494","https://openalex.org/W621782861","https://openalex.org/W2156516121","https://openalex.org/W2398840648","https://openalex.org/W1970630090","https://openalex.org/W2108781142","https://openalex.org/W1980424184","https://openalex.org/W2076599430"],"abstract_inverted_index":{"A":[0],"graph":[1,18,28,37,53,88,127,133,148,170,188,195,200,232,244],"property":[2,54,79,134,151,196],"is":[3,8,49,104,162,190,202,234,250],"called":[4],"monotone":[5,17,36,52,194,243],"if":[6],"it":[7,249],"closed":[9],"under":[10],"removal":[11],"of":[12,22,34,78,86,101,107,110,139,155,159,167,211,242,258],"edges":[13],"and":[14,30,61,81,129,150],"vertices.":[15],"Many":[16],"properties":[19,26,38,89,128,171,245],"are":[20,154],"some":[21],"the":[23,31,76,84,99,102,164,226,259],"most":[24],"well-studied":[25,87],"in":[27,46,75,123,130,147,186],"theory,":[29,189],"abstract":[32],"family":[33],"all":[35,125],"was":[39],"also":[40,82,143],"extensively":[41],"studied.":[42],"Our":[43],"main":[44,115],"result":[45,70],"this":[47,118],"paper":[48],"that":[50,90,163,191,201],"any":[51,193,199],"can":[55],"be":[56,96,121,176],"tested":[57],"with":[58,62,172],"one-sided":[59,173],"error,":[60],"query":[63,165],"complexity":[64,166],"depending":[65,213],"only":[66],"on":[67,214],"$\\epsilon$.":[68],"This":[69],"unifies":[71],"several":[72],"previous":[73,184],"results":[74,146,161,185],"area":[77],"testing":[80,168],"implies":[83],"testability":[85],"were":[91],"previously":[92],"not":[93,219],"known":[94],"to":[95],"testable.":[97],"At":[98],"heart":[100],"proof":[103],"an":[105],"application":[106,119],"a":[108,137,209,231,238],"variant":[109],"Szemer\u00e9di's":[111],"regularity":[112],"lemma.":[113],"The":[114],"ideas":[116],"behind":[117],"may":[120,175],"useful":[122],"characterizing":[124],"testable":[126,169],"generally":[131],"studying":[132],"testing.":[135],"As":[136],"byproduct":[138],"our":[140],"techniques":[141],"we":[142,224],"obtain":[144],"additional":[145],"theory":[149],"testing,":[152],"which":[153,181,217],"independent":[156],"interest.":[157],"One":[158],"these":[160],"error":[174],"arbitrarily":[177],"large.":[178],"Another":[179],"result,":[180],"significantly":[182],"extends":[183],"extremal":[187],"for":[192],"${\\cal":[197,206,221,246],"P}$,":[198,247],"$\\epsilon$-far":[203,235],"from":[204,236,255],"satisfying":[205,237,256],"P}$":[207],"contains":[208],"subgraph":[210],"size":[212],"$\\epsilon$":[215],"only,":[216],"does":[218],"satisfy":[220],"P}$.":[222],"Finally,":[223],"prove":[225],"following":[227],"compactness":[228],"statement:":[229],"If":[230],"G":[233],"(possibly":[239],"infinite)":[240],"set":[241],"then":[248],"at":[251],"least":[252],"$\\delta_{{\\cal":[253],"P}}(\\epsilon)$-far":[254],"one":[257],"properties.":[260]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
