{"id":"https://openalex.org/W1161065234","doi":"https://doi.org/10.37236/5723","title":"Chip Games and Paintability","display_name":"Chip Games and Paintability","publication_year":2016,"publication_date":"2016-07-08","ids":{"openalex":"https://openalex.org/W1161065234","doi":"https://doi.org/10.37236/5723","mag":"1161065234"},"language":"en","primary_location":{"id":"doi:10.37236/5723","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5723","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i3p3/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i3p3/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030105293","display_name":"Lech Duraj","orcid":"https://orcid.org/0000-0002-0004-3751"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Lech Duraj","raw_affiliation_strings":["Theoretical Computer Science\r\nFaculty of Mathematics and Computer Science\r\nJagiellonian University, Krak\u00f3w, Poland","Theoretical Computer Science#R##N#Faculty of Mathematics and Computer Science#R##N#Jagiellonian University, Krak\u00f3w, Poland"],"affiliations":[{"raw_affiliation_string":"Theoretical Computer Science\r\nFaculty of Mathematics and Computer Science\r\nJagiellonian University, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]},{"raw_affiliation_string":"Theoretical Computer Science#R##N#Faculty of Mathematics and Computer Science#R##N#Jagiellonian University, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038250666","display_name":"Grzegorz Gutowski","orcid":"https://orcid.org/0000-0003-3313-1237"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Grzegorz Gutowski","raw_affiliation_strings":["Theoretical Computer Science\r\nFaculty of Mathematics and Computer Science\r\nJagiellonian University, Krak\u00f3w, Poland","Theoretical Computer Science#R##N#Faculty of Mathematics and Computer Science#R##N#Jagiellonian University, Krak\u00f3w, Poland"],"affiliations":[{"raw_affiliation_string":"Theoretical Computer Science\r\nFaculty of Mathematics and Computer Science\r\nJagiellonian University, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]},{"raw_affiliation_string":"Theoretical Computer Science#R##N#Faculty of Mathematics and Computer Science#R##N#Jagiellonian University, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062623221","display_name":"Jakub Kozik","orcid":"https://orcid.org/0000-0002-1362-7780"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Jakub Kozik","raw_affiliation_strings":["Theoretical Computer Science\r\nFaculty of Mathematics and Computer Science\r\nJagiellonian University, Krak\u00f3w, Poland","Theoretical Computer Science#R##N#Faculty of Mathematics and Computer Science#R##N#Jagiellonian University, Krak\u00f3w, Poland"],"affiliations":[{"raw_affiliation_string":"Theoretical Computer Science\r\nFaculty of Mathematics and Computer Science\r\nJagiellonian University, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]},{"raw_affiliation_string":"Theoretical Computer Science#R##N#Faculty of Mathematics and Computer Science#R##N#Jagiellonian University, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5030105293"],"corresponding_institution_ids":["https://openalex.org/I126596746"],"apc_list":null,"apc_paid":null,"fwci":1.0773,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.84245466,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"23","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11161","display_name":"Consumer Market Behavior and Pricing","score":0.9205999970436096,"subfield":{"id":"https://openalex.org/subfields/1406","display_name":"Marketing"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11161","display_name":"Consumer Market Behavior and Pricing","score":0.9205999970436096,"subfield":{"id":"https://openalex.org/subfields/1406","display_name":"Marketing"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T13402","display_name":"Business Strategy and Innovation","score":0.9104999899864197,"subfield":{"id":"https://openalex.org/subfields/1408","display_name":"Strategy and Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.8299334645271301},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.7654992341995239},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7122239470481873},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6604859232902527},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6161969900131226},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5100229382514954},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5059930682182312},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45127055048942566},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.4444693922996521},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.415127158164978},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.4136263430118561},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27358686923980713},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05057474970817566}],"concepts":[{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.8299334645271301},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.7654992341995239},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7122239470481873},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6604859232902527},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6161969900131226},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5100229382514954},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5059930682182312},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45127055048942566},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.4444693922996521},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.415127158164978},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.4136263430118561},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27358686923980713},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05057474970817566},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/5723","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5723","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i3p3/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1506.01148","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1506.01148","pdf_url":"https://arxiv.org/pdf/1506.01148","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:1161065234","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1506.01148","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:ruj.uj.edu.pl:item/33418","is_oa":false,"landing_page_url":"http://www.combinatorics.org/ojs/index.php/eljc/article/view/v23i3p3/pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400316","display_name":"Homo Politicus (Academy of Humanities and Economics in Lodz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"artyku\u0142 w czasopi\u015bmie"},{"id":"doi:10.48550/arxiv.1506.01148","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1506.01148","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.37236/5723","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5723","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i3p3/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W1161065234.pdf"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2039241885","https://openalex.org/W2054837106"],"related_works":["https://openalex.org/W2804115786","https://openalex.org/W2949820550","https://openalex.org/W3136471880","https://openalex.org/W2229530913","https://openalex.org/W3134481349","https://openalex.org/W2398655068","https://openalex.org/W1524011893","https://openalex.org/W2130919080","https://openalex.org/W1785707220","https://openalex.org/W2949949886","https://openalex.org/W3003330899","https://openalex.org/W2084548401","https://openalex.org/W2054605652","https://openalex.org/W1983547967","https://openalex.org/W2108315684","https://openalex.org/W25440674","https://openalex.org/W3197676983","https://openalex.org/W2951923114","https://openalex.org/W58963464","https://openalex.org/W2112298758"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2,22,82],"the":[3,7,23,26,30,42,44,70,99],"paint":[4,27],"number":[5,28,32],"of":[6,33,46,72,75,109,113],"complete":[8],"bipartite":[9],"graph":[10],"$K_{N,N}$":[11,34],"is":[12,35],"$\\log":[13],"N":[14],"+":[15],"O(1)$.":[16],"As":[17],"a":[18,59,63,91,110],"consequence,":[19],"we":[20,80],"get":[21],"difference":[24],"between":[25],"and":[29],"choice":[31],"$\\Theta(\\log":[36],"\\log":[37],"N)$.":[38],"This":[39,78],"answers":[40],"in":[41],"negative":[43],"question":[45],"Zhu":[47],"(2009)":[48],"whether":[49],"this":[50],"difference,":[51],"for":[52,83],"all":[53],"graphs,":[54],"can":[55],"be":[56],"bounded":[57],"by":[58],"common":[60],"constant.":[61],"By":[62],"classical":[64],"correspondence,":[65],"our":[66],"result":[67],"translates":[68],"to":[69],"framework":[71],"on-line":[73,85],"coloring":[74,87],"uniform":[76],"hypergraphs.":[77],"way":[79],"obtain":[81],"every":[84],"two":[86],"algorithm":[88],"there":[89],"exists":[90],"$k$-uniform":[92],"hypergraph":[93],"with":[94],"$\\Theta(2^k)$":[95],"edges":[96],"on":[97],"which":[98],"strategy":[100],"fails.":[101],"The":[102],"results":[103],"are":[104],"derived":[105],"through":[106],"an":[107],"analysis":[108],"natural":[111],"family":[112],"chip":[114],"games.":[115]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
