{"id":"https://openalex.org/W1956452579","doi":"https://doi.org/10.1137/100786290","title":"Boxicity and Poset Dimension","display_name":"Boxicity and Poset Dimension","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1956452579","doi":"https://doi.org/10.1137/100786290","mag":"1956452579"},"language":"en","primary_location":{"id":"doi:10.1137/100786290","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100786290","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","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/A5019703184","display_name":"Abhijin Adiga","orcid":"https://orcid.org/0000-0002-9770-034X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Abhijin Adiga","raw_affiliation_strings":["abhijin@csa.iisc.ernet.in and diptendubhowmick@gmail.com and sunil@csa.iisc.ernet.in#TAB#"],"affiliations":[{"raw_affiliation_string":"abhijin@csa.iisc.ernet.in and diptendubhowmick@gmail.com and sunil@csa.iisc.ernet.in#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056606992","display_name":"Diptendu Bhowmick","orcid":null},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Diptendu Bhowmick","raw_affiliation_strings":["Dept of Computer Science & Automation, Indian Institute of Science, Bangalore, India#TAB#"],"affiliations":[{"raw_affiliation_string":"Dept of Computer Science & Automation, Indian Institute of Science, Bangalore, India#TAB#","institution_ids":["https://openalex.org/I59270414"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024359075","display_name":"L. Sunil Chandran","orcid":"https://orcid.org/0000-0001-5451-6975"},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"L. Sunil Chandran","raw_affiliation_strings":["Dept of Computer Science & Automation, Indian Institute of Science, Bangalore, India#TAB#"],"affiliations":[{"raw_affiliation_string":"Dept of Computer Science & Automation, Indian Institute of Science, Bangalore, India#TAB#","institution_ids":["https://openalex.org/I59270414"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5019703184"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5545,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.92472568,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"25","issue":"4","first_page":"1687","last_page":"1698"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9980999827384949,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9980999827384949,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9962000250816345,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9914000034332275,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8992795348167419},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7619075775146484},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.7349827289581299},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.7221922874450684},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5803446173667908},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4724857211112976},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47219526767730713},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4231707453727722}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8992795348167419},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7619075775146484},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.7349827289581299},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.7221922874450684},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5803446173667908},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4724857211112976},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47219526767730713},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4231707453727722},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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":1,"locations":[{"id":"doi:10.1137/100786290","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100786290","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","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":26,"referenced_works":["https://openalex.org/W161777220","https://openalex.org/W1603384057","https://openalex.org/W1606702051","https://openalex.org/W1971244706","https://openalex.org/W1971431042","https://openalex.org/W1974534721","https://openalex.org/W1978848148","https://openalex.org/W1985734960","https://openalex.org/W1987554952","https://openalex.org/W2013288868","https://openalex.org/W2021339822","https://openalex.org/W2029628171","https://openalex.org/W2033520777","https://openalex.org/W2034198559","https://openalex.org/W2047899424","https://openalex.org/W2068530335","https://openalex.org/W2085486788","https://openalex.org/W2096001230","https://openalex.org/W2106120818","https://openalex.org/W2122913936","https://openalex.org/W2134744951","https://openalex.org/W2138222093","https://openalex.org/W2143474538","https://openalex.org/W2325654786","https://openalex.org/W2400180097","https://openalex.org/W3145128584"],"related_works":["https://openalex.org/W2106070061","https://openalex.org/W2805171307","https://openalex.org/W4378978929","https://openalex.org/W4366733366","https://openalex.org/W3137798114","https://openalex.org/W4378087371","https://openalex.org/W2364608040","https://openalex.org/W2998748068","https://openalex.org/W1983442375","https://openalex.org/W3190844188"],"abstract_inverted_index":{"Let":[0,76,122,322],"G":[1,41,67,250],"be":[2,43,78,113,124,324,394],"a":[3,20,58,79,90,153,178,218,231,235,248,252,271,451,457,472,479],"simple,":[4],"undirected,":[5],"finite":[6],"graph":[7,48,128,163,229,249,273,390,424,458,474],"with":[8,158,251,257,274,330,425,446,478],"vertex":[9,54,135],"set":[10,14,86,136,336,343],"$V(G)$":[11,284],"and":[12,61,69,87,93,137,143,209,278,298,301,309,340,360],"edge":[13,305],"$E(G)$.":[15],"A":[16,277,334],"k-dimensional":[17,50,59],"box":[18,60],"is":[19,34,55,83,89,104,133,152,203,217,234,270,303,316,391,429,432,459],"Cartesian":[21],"product":[22],"of":[23,31,49,101,118,129,171,177,183,207,230,241,247,262,283,337,344,388,422,440,456,471,481],"closed":[24],"intervals":[25],"$[a_1,b_1]\\times":[26],"[a_2,b_2]\\times\\cdots\\times":[27],"[a_k,b_k]$.":[28],"The":[29,99,168,238,363,420],"boxicity":[30,182,246,387,421,447,455,470],"G,":[32,263],"box$(G)$,":[33],"the":[35,46,84,105,116,125,134,159,165,175,181,204,226,242,245,258,325,335,342,403,407,417,436,454,469],"minimum":[36,106],"integer":[37,107],"k":[38],"such":[39,109,285,379],"that":[40,110,156,192,214,268,349,453],"can":[42,112],"represented":[44],"as":[45,115,265,380],"intersection":[47,117],"boxes;":[51],"i.e.,":[52,131],"each":[53],"mapped":[56],"to":[57,180,288,318,370,393,467],"two":[62,138,294],"vertices":[63,139,295,477],"are":[64,140,147,281,293],"adjacent":[65,141,317],"in":[66,149,306,320],"if":[68,71,142,145,215,308,311],"only":[70,144,310],"their":[72],"corresponding":[73,287],"boxes":[74],"intersect.":[75],"$\\mathcal{P}=(S,P)$":[77],"poset,":[80,220],"where":[81,201],"S":[82,132],"ground":[85],"P":[88,111],"reflexive,":[91],"antisymmetric":[92],"transitive":[94],"binary":[95],"relation":[96],"on":[97,475],"S.":[98],"dimension":[100,176,378,414],"$\\mathcal{P}$,":[102,196],"$\\dim(\\mathcal{P})$,":[103],"t":[108,119],"expressed":[114],"total":[120],"orders.":[121],"$G_{\\mathcal{P}}$":[123,208],"underlying":[126,161,185,227],"comparability":[127,162,186,228],"$\\mathcal{P}$;":[130],"they":[146],"comparable":[148],"$\\mathcal{P}$.":[150],"It":[151,211],"well-known":[154],"fact":[155],"posets":[157],"same":[160,166],"have":[164,357],"dimension.":[167],"first":[169],"result":[170,240],"this":[172],"paper":[173,243],"links":[174],"poset":[179,195,233,328,377],"its":[184,397],"graph.":[187,237],"In":[188,402],"particular,":[189],"we":[190,415],"show":[191,348],"for":[193,376,411,483],"any":[194,389,423,484],"box$(G_{\\mathcal{P}})/(\\chi(G_{\\mathcal{P}})-1)":[197],"\\le":[198,351,353],"\\dim(\\mathcal{P})\\le":[199,223],"2\\mbox{box}(G_{\\mathcal{P}})$,":[200],"$\\chi(G_{\\mathcal{P}})$":[202],"chromatic":[205],"number":[206],"$\\chi(G_{\\mathcal{P}})\\ne1$.":[210],"immediately":[212],"follows":[213],"$\\mathcal{P}$":[216],"height-2":[219,232,327],"then":[221],"box$(G_{\\mathcal{P}})\\le":[222],"2\\mbox{box}(G_{\\mathcal{P}})$":[224],"since":[225,386],"bipartite":[236,272,473],"second":[239],"relates":[244],"natural":[253,326],"partial":[254,412],"order":[255,413],"associated":[256,329],"extended":[259],"double":[260],"cover":[261],"denoted":[264],"$G_c$:":[266],"Note":[267],"$G_c$":[269,307,331],"partite":[275],"sets":[276],"B":[279,341],"which":[280,431],"copies":[282],"that,":[286],"every":[289],"$u\\in":[290],"V(G)$,":[291],"there":[292],"$u_A\\in":[296],"A$":[297],"$u_B\\in":[299],"B$":[300],"$\\{u_A,v_B\\}$":[302],"an":[304,433],"either":[312],"$u=v$":[313],"or":[314],"u":[315],"v":[319],"G.":[321],"$\\mathcal{P}_c$":[323],"by":[332],"making":[333],"minimal":[338],"elements":[339],"maximal":[345],"elements.":[346],"We":[347],"$\\frac{\\mbox{box}(G)}{2}":[350],"\\dim(\\mathcal{P}_c)":[352],"2\\mbox{box}(G)+4$.":[354],"These":[355],"results":[356],"some":[358],"immediate":[359],"significant":[361],"consequences.":[362],"upper":[364,374,438],"bound":[365,439],"$\\dim(\\mathcal{P})\\le":[366,381],"2\\mbox{box}(G_\\mathcal{P})$":[367],"allows":[368],"us":[369],"derive":[371],"hitherto":[372],"unknown":[373],"bounds":[375,410],"2\\mbox{":[382],"tree":[383,398],"width":[384,399],"}(G_{\\mathcal{P}})+4$,":[385],"known":[392,409],"at":[395],"most":[396],"$+\\;":[400],"2$.":[401],"other":[404],"direction,":[405],"using":[406],"already":[408],"get":[416],"following:":[418],"(1)":[419],"maximum":[426],"degree":[427],"$\\Delta$":[428],"$O(\\Delta\\log^2\\Delta)$,":[430],"improvement":[434],"over":[435],"best-known":[437],"$\\Delta^2+2$.":[441],"(2)":[442],"There":[443,462],"exist":[444],"graphs":[445],"$\\Omega(\\Delta\\log\\Delta)$.":[448],"This":[449],"disproves":[450],"conjecture":[452],"$O(\\Delta)$.":[460],"(3)":[461],"exists":[463],"no":[464],"polynomial-time":[465],"algorithm":[466],"approximate":[468],"n":[476],"factor":[480],"$O(n^{0.5-\\epsilon})$":[482],"$\\epsilon>0$":[485],"unless":[486],"$NP=ZPP$.":[487]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
