{"id":"https://openalex.org/W2123878503","doi":"https://doi.org/10.1109/ccc.2002.1004336","title":"Resolution lower bounds for perfect matching principles","display_name":"Resolution lower bounds for perfect matching principles","publication_year":2003,"publication_date":"2003-06-25","ids":{"openalex":"https://openalex.org/W2123878503","doi":"https://doi.org/10.1109/ccc.2002.1004336","mag":"2123878503"},"language":"en","primary_location":{"id":"doi:10.1109/ccc.2002.1004336","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ccc.2002.1004336","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings 17th IEEE Annual Conference on Computational Complexity","raw_type":"proceedings-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/A5008113826","display_name":"Alexander Razborov","orcid":null},"institutions":[{"id":"https://openalex.org/I40036882","display_name":"Institute for Advanced Study","ror":"https://ror.org/00f809463","country_code":"US","type":"facility","lineage":["https://openalex.org/I40036882"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A.A. Razborov","raw_affiliation_strings":["Institute of Advanced Study in Science and Technology, Princeton, NJ, USA","Inst. for Adv. Study, Princeton, NJ, USA"],"affiliations":[{"raw_affiliation_string":"Institute of Advanced Study in Science and Technology, Princeton, NJ, USA","institution_ids":["https://openalex.org/I40036882"]},{"raw_affiliation_string":"Inst. for Adv. Study, Princeton, NJ, USA","institution_ids":["https://openalex.org/I40036882"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5008113826"],"corresponding_institution_ids":["https://openalex.org/I40036882"],"apc_list":null,"apc_paid":null,"fwci":5.3174,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.9614824,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"39","issue":null,"first_page":"29","last_page":"38"},"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":0.9995999932289124,"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":0.9896000027656555,"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/combinatorics","display_name":"Combinatorics","score":0.8385531306266785},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.7040458917617798},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5995545387268066},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5249814391136169},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.5244379639625549},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.45638707280158997},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.4427040219306946},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.4331378638744354},{"id":"https://openalex.org/keywords/pigeonhole-principle","display_name":"Pigeonhole principle","score":0.41926804184913635},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41759756207466125},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4102926254272461},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3401648998260498},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.19354316592216492},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08986112475395203},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08136817812919617}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8385531306266785},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.7040458917617798},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5995545387268066},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5249814391136169},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.5244379639625549},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.45638707280158997},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.4427040219306946},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.4331378638744354},{"id":"https://openalex.org/C171988527","wikidata":"https://www.wikidata.org/wiki/Q188276","display_name":"Pigeonhole principle","level":2,"score":0.41926804184913635},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41759756207466125},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4102926254272461},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3401648998260498},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.19354316592216492},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08986112475395203},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08136817812919617},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ccc.2002.1004336","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ccc.2002.1004336","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings 17th IEEE Annual Conference on Computational Complexity","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W19485686","https://openalex.org/W157950381","https://openalex.org/W256057417","https://openalex.org/W270222139","https://openalex.org/W1557604257","https://openalex.org/W1564324806","https://openalex.org/W1568798323","https://openalex.org/W1607926272","https://openalex.org/W1902951782","https://openalex.org/W1966153097","https://openalex.org/W1979753555","https://openalex.org/W2006367699","https://openalex.org/W2084384424","https://openalex.org/W2090339500","https://openalex.org/W2093396771","https://openalex.org/W2098022011","https://openalex.org/W2110053319","https://openalex.org/W2134961930","https://openalex.org/W2143313747","https://openalex.org/W2407913417","https://openalex.org/W2985554528","https://openalex.org/W4248733413","https://openalex.org/W6606399963","https://openalex.org/W6609571330","https://openalex.org/W6609908499","https://openalex.org/W6634145069"],"related_works":["https://openalex.org/W1902951782","https://openalex.org/W1521859395","https://openalex.org/W2041857712","https://openalex.org/W256057417","https://openalex.org/W2090339500","https://openalex.org/W2026967932","https://openalex.org/W2029390834","https://openalex.org/W2062058334","https://openalex.org/W4213091458","https://openalex.org/W2535850430"],"abstract_inverted_index":{"For":[0,73],"an":[1,57,138],"arbitrary":[2],"hypergraph":[3],"H":[4,13,201],"let":[5],"PM(H)":[6,25],"be":[7],"the":[8,38,45,53,63,97,103,126,145,151,158,162],"propositional":[9],"formula":[10],"asserting":[11,156,199],"that":[12,20,157,200],"contains":[14,202],"a":[15,49,90,100,191,203],"perfect":[16],"matching.":[17],"We":[18],"show":[19],"every":[21,93],"resolution":[22,94,148,176],"refutation":[23],"of":[24,40,48,56,66,96,102,128,147,150,161,182],"must":[26,111],"have":[27,112],"size":[28,55,113,146,160],"exp((/spl":[29],"Omega/(/spl":[30,85],"delta/(H)//spl":[31],"lambda/(H)r(H)(log":[32],"n(H))(r(H)+log":[33],"n(H)))),":[34],"where":[35],"n(H)":[36],"is":[37,44,52,62,131,170],"number":[39,65,127],"vertices,":[41],"/spl":[42,60,184,210],"delta/(H)":[43],"minimal":[46],"degree":[47],"vertex,":[50],"r(H)":[51],"maximal":[54,64],"edge,":[58],"and":[59],"lambda/(H)":[61],"edges":[67],"incident":[68],"to":[69,82,194],"two":[70],"different":[71],"vertices.":[72],"ordinary":[74],"graphs":[75],"G":[76],"our":[77],"general":[78,196],"bound":[79,143],"considerably":[80],"simplifies":[81],"exp":[83,114,121],"(/spl":[84,115,122],"delta/(G)/(log":[86],"n(G))/sup":[87],"2/))).":[88],"As":[89],"direct":[91],"corollary,":[92],"proof":[95],"functional":[98],"onto":[99,106],"version":[101],"pigeonhole":[104],"principle":[105,152,197],"-":[107],"FPHP/sub":[108],"n//sup":[109],"m/":[110],"Omega/(n/(log":[116],"m)/sup":[117],"2/))":[118],"(which":[119],"becomes":[120],"Omega/(n/sup":[123],"1/3/))":[124],"when":[125],"pigeons":[129],"m":[130],"unbounded).":[132],"This":[133],"in":[134,167,190,208],"turn":[135],"immediately":[136],"implies":[137],"exp(/spl":[139],"Omega/(t/n/sup":[140],"3/))":[141],"lower":[142],"on":[144],"proofs":[149,181],"circuit/sub":[153],"t/(f/sub":[154],"n/)":[155],"circuit":[159],"Boolean":[163],"function":[164],"f/sub":[165],"n/":[166],"n":[168],"variables":[169],"greater":[171],"than":[172],"t.":[173],"In":[174],"particular":[175],"does":[177],"not":[178],"possess":[179],"efficient":[180],"NP":[183],"subne/":[185],"P/poly.":[186],"These":[187],"results":[188],"relativize,":[189],"natural":[192],"way,":[193],"more":[195],"M(U|H)":[198],"matching":[204],"covering":[205],"all":[206],"vertices":[207],"U":[209],"sube/":[211],"V(H).":[212]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
