{"id":"https://openalex.org/W300087758","doi":"https://doi.org/10.1007/s00493-014-2367-1","title":"Constructing Ramsey Graphs from Boolean Function Representations","display_name":"Constructing Ramsey Graphs from Boolean Function Representations","publication_year":2006,"publication_date":"2006-08-08","ids":{"openalex":"https://openalex.org/W300087758","doi":"https://doi.org/10.1007/s00493-014-2367-1","mag":"300087758"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-014-2367-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-014-2367-1","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","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/A5036468719","display_name":"Parikshit Gopalan","orcid":null},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I4210086253","display_name":"Silicon Valley Community Foundation","ror":"https://ror.org/001ader08","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210086253"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Parikshit Gopalan","raw_affiliation_strings":["Microsoft Research \u2014 Silicon Valley, Mountain View, CA, 94043, USA","Microsoft Research, Silicon Valley, Mountain View, USA 94043#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research \u2014 Silicon Valley, Mountain View, CA, 94043, USA","institution_ids":["https://openalex.org/I1290206253","https://openalex.org/I4210086253"]},{"raw_affiliation_string":"Microsoft Research, Silicon Valley, Mountain View, USA 94043#TAB#","institution_ids":["https://openalex.org/I1290206253"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036468719"],"corresponding_institution_ids":["https://openalex.org/I1290206253","https://openalex.org/I4210086253"],"apc_list":{"value":3290,"currency":"USD","value_usd":3290},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.01344688,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"34","issue":"2","first_page":"115","last_page":"128"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","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/T10374","display_name":"Advanced Graph Theory Research","score":0.9987000226974487,"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/mathematics","display_name":"Mathematics","score":0.7538715600967407},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.665336012840271},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.546137809753418},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5006308555603027},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.4552612900733948},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.4375031292438507},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.41176605224609375},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.4114045798778534},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.41022759675979614}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7538715600967407},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.665336012840271},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.546137809753418},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5006308555603027},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.4552612900733948},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.4375031292438507},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.41176605224609375},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.4114045798778534},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.41022759675979614},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1007/s00493-014-2367-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-014-2367-1","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},{"id":"doi:10.1109/ccc.2006.14","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ccc.2006.14","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"21st Annual IEEE Conference on Computational Complexity (CCC'06)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.514.3807","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.514.3807","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://research.microsoft.com/pubs/77676/eccc.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.62.3542","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.62.3542","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cc.gatech.edu/~parik/RESEARCH/ramsey.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.67.6793","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.67.6793","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cc.gatech.edu/~parik/RESEARCH/ramsey-full.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.72.5073","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.72.5073","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cc.gatech.edu/~parik/RESEARCH/ramsey-full.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.94.9190","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.94.9190","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eccc.hpi-web.de/eccc-reports/2005/TR05-143/Paper.pdf","raw_type":"text"},{"id":"mag:300087758","is_oa":false,"landing_page_url":"http://dblp.uni-trier.de/db/journals/eccc/eccc12.html#TR05-143","pdf_url":null,"source":{"id":"https://openalex.org/S11189987","display_name":"Electronic colloquium on computational complexity","issn_l":"1433-8092","issn":["1433-8092"],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":"Electronic colloquium on computational complexity","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1554708489","https://openalex.org/W1966440495","https://openalex.org/W1998698985","https://openalex.org/W2000118462","https://openalex.org/W2030052209","https://openalex.org/W2039991502","https://openalex.org/W2045472305","https://openalex.org/W2047230132","https://openalex.org/W2054996571","https://openalex.org/W2060276273","https://openalex.org/W2064197162","https://openalex.org/W2068871408","https://openalex.org/W2069582894","https://openalex.org/W2084622077","https://openalex.org/W2097114401","https://openalex.org/W2102801247","https://openalex.org/W2123114890","https://openalex.org/W2135963330","https://openalex.org/W2140644794","https://openalex.org/W2142610181","https://openalex.org/W2142818154","https://openalex.org/W2157443379","https://openalex.org/W2229615128","https://openalex.org/W2404981435","https://openalex.org/W2972131259","https://openalex.org/W4249721970","https://openalex.org/W6601867708","https://openalex.org/W6610744021"],"related_works":["https://openalex.org/W1996712932","https://openalex.org/W2764159756","https://openalex.org/W2751958198","https://openalex.org/W2949641092","https://openalex.org/W3123619251","https://openalex.org/W2770992319","https://openalex.org/W2065259354","https://openalex.org/W2296666114","https://openalex.org/W2949231286","https://openalex.org/W2073590727","https://openalex.org/W1591975452","https://openalex.org/W3098159482","https://openalex.org/W2080817296","https://openalex.org/W3082232217","https://openalex.org/W2903099655","https://openalex.org/W2269054999","https://openalex.org/W2951111775","https://openalex.org/W1560723985","https://openalex.org/W2922255736","https://openalex.org/W2949770641"],"abstract_inverted_index":{"Explicit":[0],"construction":[1,128,192],"of":[2,31,41,62,98,103,112,129,170,193],"Ramsey":[3,54,79,131,182],"graphs":[4,6,32,55,80],"or":[5,11,38],"with":[7,35],"no":[8,36],"large":[9],"clique":[10,37],"independent":[12,39],"set":[13,40],"has":[14],"remained":[15],"a":[16,21,49,65,90,95,101,126,130],"challenging":[17],"open":[18],"problem":[19],"for":[20,69],"long":[22],"time.":[23],"While":[24],"Erdos'":[25],"probabilistic":[26],"argument":[27],"shows":[28],"the":[29,44,70,85,106,110,122,141,178,191],"existence":[30],"on":[33,174],"2nvertices":[34],"size":[42],"2n,":[43],"best":[45],"explicit":[46],"constructions":[47,183],"achieve":[48],"far":[50],"weaker":[51],"bound.":[52],"Constructing":[53],"is":[56],"closely":[57],"related":[58],"to":[59,76,146,148,180,189],"polynomial":[60],"representations":[61,169],"Boolean":[63],"functions;":[64],"low":[66],"degree":[67,171,195],"representation":[68],"OR":[71,99,107,168],"function":[72,108],"can":[73,162],"be":[74,164,190,207],"used":[75],"explicitly":[77],"construct":[78],"(Grolmusz,":[81],"2000).":[82],"We":[83,93,124],"generalize":[84],"above":[86],"relation":[87],"by":[88,158],"proposing":[89],"new":[91,96,198],"framework.":[92],"propose":[94],"definition":[97],"representations:":[100],"pair":[102],"polynomials":[104,211],"represent":[105],"if":[109],"union":[111],"their":[113],"zero":[114],"sets":[115],"contains":[116],"all":[117,140,163],"points":[118],"in":[119],"{0,":[120],"1}nexcept":[121],"origin.":[123],"give":[125],"simple":[127],"graph":[132],"using":[133,209],"such":[134,185],"polynomials.":[135,176],"Furthermore,":[136],"we":[137,201],"show":[138,202],"that":[139,203],"known":[142],"algebraic":[143,186,199],"constructions,":[144],"ones":[145],"due":[147],"Frankl-Wilson":[149],"(1981),":[150],"Grolmusz":[151],"(2000)":[152],"and":[153],"Alon":[154],"(1998)":[155],"are":[156],"captured":[157],"this":[159],"framework;":[160],"they":[161],"derived":[165],"from":[166],"various":[167],"O(radicn)":[172],"based":[173],"symmetric":[175,210],"Thus":[177],"barrier":[179],"better":[181,204],"through":[184],"methods":[187],"appears":[188],"lower":[194],"representations.":[196],"Using":[197],"techniques,":[200],"bounds":[205],"cannot":[206],"obtained":[208]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}