{"id":"https://openalex.org/W4237717242","doi":"https://doi.org/10.37236/1948","title":"Discrepancy Games","display_name":"Discrepancy Games","publication_year":2005,"publication_date":"2005-09-29","ids":{"openalex":"https://openalex.org/W4237717242","doi":"https://doi.org/10.37236/1948"},"language":"en","primary_location":{"id":"doi:10.37236/1948","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1948","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1r51/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1r51/pdf","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":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]},{"id":"https://openalex.org/I4210107917","display_name":"Exact Sciences (United States)","ror":"https://ror.org/01kc31v38","country_code":"US","type":"company","lineage":["https://openalex.org/I4210107917"]},{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["CH","IL","US"],"is_corresponding":true,"raw_author_name":"Noga Alon","raw_affiliation_strings":["Schools of Mathematics and Computer Science Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, Tel Aviv 69978, Israel and IAS, Princeton, NJ 08540, USA","Institut f\u00fcr Theoretische Informatik ETH Zentrum, IFW B48.1, CH -8092 Z\u00fcrich, Switzerland","Department of Mathematics and Computer Science Courant Institute, NYU, NY, USA","School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, Tel Aviv 69978, Israel"],"affiliations":[{"raw_affiliation_string":"Schools of Mathematics and Computer Science Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, Tel Aviv 69978, Israel and IAS, Princeton, NJ 08540, USA","institution_ids":["https://openalex.org/I4210107917","https://openalex.org/I16391192"]},{"raw_affiliation_string":"Institut f\u00fcr Theoretische Informatik ETH Zentrum, IFW B48.1, CH -8092 Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science Courant Institute, NYU, NY, USA","institution_ids":["https://openalex.org/I36672615"]},{"raw_affiliation_string":"School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, Tel Aviv 69978, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102759207","display_name":"Michael Krivelevich","orcid":null},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]},{"id":"https://openalex.org/I4210107917","display_name":"Exact Sciences (United States)","ror":"https://ror.org/01kc31v38","country_code":"US","type":"company","lineage":["https://openalex.org/I4210107917"]},{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]},{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["CH","IL","US"],"is_corresponding":false,"raw_author_name":"Michael Krivelevich","raw_affiliation_strings":["Department of Mathematics and Computer Science Courant Institute, NYU, NY, USA","Institut f\u00fcr Theoretische Informatik ETH Zentrum, IFW B48.1, CH -8092 Z\u00fcrich, Switzerland","School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, Tel Aviv 69978, Israel","Schools of Mathematics and Computer Science Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, Tel Aviv 69978, Israel and IAS, Princeton, NJ 08540, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science Courant Institute, NYU, NY, USA","institution_ids":["https://openalex.org/I36672615"]},{"raw_affiliation_string":"Institut f\u00fcr Theoretische Informatik ETH Zentrum, IFW B48.1, CH -8092 Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, Tel Aviv 69978, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Schools of Mathematics and Computer Science Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, Tel Aviv 69978, Israel and IAS, Princeton, NJ 08540, USA","institution_ids":["https://openalex.org/I4210107917","https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112765534","display_name":"Joel Spencer","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]},{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]},{"id":"https://openalex.org/I4210107917","display_name":"Exact Sciences (United States)","ror":"https://ror.org/01kc31v38","country_code":"US","type":"company","lineage":["https://openalex.org/I4210107917"]},{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["CH","IL","US"],"is_corresponding":false,"raw_author_name":"Joel Spencer","raw_affiliation_strings":["School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, Tel Aviv 69978, Israel","Department of Mathematics and Computer Science Courant Institute, NYU, NY, USA","Schools of Mathematics and Computer Science Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, Tel Aviv 69978, Israel and IAS, Princeton, NJ 08540, USA","Institut f\u00fcr Theoretische Informatik ETH Zentrum, IFW B48.1, CH -8092 Z\u00fcrich, Switzerland"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, Tel Aviv 69978, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science Courant Institute, NYU, NY, USA","institution_ids":["https://openalex.org/I36672615"]},{"raw_affiliation_string":"Schools of Mathematics and Computer Science Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, Tel Aviv 69978, Israel and IAS, Princeton, NJ 08540, USA","institution_ids":["https://openalex.org/I4210107917","https://openalex.org/I16391192"]},{"raw_affiliation_string":"Institut f\u00fcr Theoretische Informatik ETH Zentrum, IFW B48.1, CH -8092 Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068960247","display_name":"Tibor Szab\u00f3","orcid":"https://orcid.org/0000-0003-0599-0624"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]},{"id":"https://openalex.org/I4210107917","display_name":"Exact Sciences (United States)","ror":"https://ror.org/01kc31v38","country_code":"US","type":"company","lineage":["https://openalex.org/I4210107917"]},{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["CH","IL","US"],"is_corresponding":false,"raw_author_name":"Tibor Szab\u00f3","raw_affiliation_strings":["Department of Mathematics and Computer Science Courant Institute, NYU, NY, USA","Institut f\u00fcr Theoretische Informatik ETH Zentrum, IFW B48.1, CH -8092 Z\u00fcrich, Switzerland","School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, Tel Aviv 69978, Israel","Schools of Mathematics and Computer Science Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, Tel Aviv 69978, Israel and IAS, Princeton, NJ 08540, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science Courant Institute, NYU, NY, USA","institution_ids":["https://openalex.org/I36672615"]},{"raw_affiliation_string":"Institut f\u00fcr Theoretische Informatik ETH Zentrum, IFW B48.1, CH -8092 Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, Tel Aviv 69978, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Schools of Mathematics and Computer Science Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, Tel Aviv 69978, Israel and IAS, Princeton, NJ 08540, USA","institution_ids":["https://openalex.org/I4210107917","https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5083469386"],"corresponding_institution_ids":["https://openalex.org/I16391192","https://openalex.org/I35440088","https://openalex.org/I36672615","https://openalex.org/I4210107917"],"apc_list":null,"apc_paid":null,"fwci":0.8757,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.73710184,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"12","issue":"1","first_page":null,"last_page":null},"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":0.9815000295639038,"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":0.9815000295639038,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9794999957084656,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.9588000178337097,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/combinatorics","display_name":"Combinatorics","score":0.827478289604187},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7524476647377014},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.7106592655181885},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6076810956001282},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.44512343406677246},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39728057384490967},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13585838675498962},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.12338387966156006},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06373339891433716}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.827478289604187},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7524476647377014},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.7106592655181885},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6076810956001282},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.44512343406677246},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39728057384490967},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13585838675498962},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.12338387966156006},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06373339891433716}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1948","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1948","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1r51/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/1948","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1948","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1r51/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7315415636","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"},{"id":"https://openalex.org/F4320322596","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4237717242.pdf","grobid_xml":"https://content.openalex.org/works/W4237717242.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W1988370884","https://openalex.org/W2062589906","https://openalex.org/W3011766368"],"related_works":["https://openalex.org/W4376608589","https://openalex.org/W3138003926","https://openalex.org/W4300037846","https://openalex.org/W1630514295","https://openalex.org/W1537073411","https://openalex.org/W2963081352","https://openalex.org/W2472555608","https://openalex.org/W3094179932","https://openalex.org/W3005801850","https://openalex.org/W2950595062"],"abstract_inverted_index":{"We":[0,51,102],"investigate":[1],"a":[2,6,53],"game":[3,38,108],"played":[4],"on":[5,96],"hypergraph":[7],"$H=(V,E)$":[8],"by":[9],"two":[10,49],"players,":[11],"Balancer":[12,30,58,85],"and":[13,80,91],"Unbalancer.":[14],"They":[15],"select":[16],"one":[17],"element":[18],"of":[19,36,93,100],"the":[20,34,37,48,62],"vertex":[21],"set":[22],"$V$":[23],"alternately":[24],"until":[25],"all":[26,39],"vertices":[27,95],"are":[28,43],"selected.":[29],"wins":[31],"if":[32,76],"at":[33],"end":[35],"edges":[40],"$e\\in":[41],"E$":[42],"roughly":[44],"equally":[45],"distributed":[46],"between":[47,89],"players.":[50],"give":[52],"polynomial":[54],"time":[55],"algorithm":[56],"for":[57],"to":[59],"win":[60],"provided":[61],"allowed":[63],"deviation":[64],"is":[65,78],"large":[66],"enough.":[67],"In":[68],"particular,":[69],"it":[70],"follows":[71],"from":[72],"our":[73],"result":[74],"that":[75],"$H$":[77],"$n$-uniform":[79],"has":[81],"$m$":[82],"edges,":[83],"then":[84],"can":[86],"achieve":[87],"having":[88],"$n/2-\\sqrt{\\ln(2m)n/2}$":[90],"$n/2+\\sqrt{\\ln(2m)n/2}$":[92],"his":[94],"every":[97],"edge":[98],"$e$":[99],"$H$.":[101],"also":[103],"discuss":[104],"applications":[105],"in":[106],"positional":[107],"theory.":[109]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2022-05-12T00:00:00"}
