{"id":"https://openalex.org/W2111091812","doi":"https://doi.org/10.1017/s0963548312000429","title":"Tur\u00e1n and Ramsey Properties of Subcube Intersection Graphs","display_name":"Tur\u00e1n and Ramsey Properties of Subcube Intersection Graphs","publication_year":2012,"publication_date":"2012-10-03","ids":{"openalex":"https://openalex.org/W2111091812","doi":"https://doi.org/10.1017/s0963548312000429","mag":"2111091812"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548312000429","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548312000429","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","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/A5111642018","display_name":"J. Robert Johnson","orcid":null},"institutions":[{"id":"https://openalex.org/I166337079","display_name":"Queen Mary University of London","ror":"https://ror.org/026zzn846","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I166337079"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"J. ROBERT JOHNSON","raw_affiliation_strings":["School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK (e-mail:","School of mathematical sciences, queen mary, university of london, london e1 4ns, uk (e-mail: r.johnson@qmul.ac.uk)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK (e-mail:","institution_ids":["https://openalex.org/I166337079"]},{"raw_affiliation_string":"School of mathematical sciences, queen mary, university of london, london e1 4ns, uk (e-mail: r.johnson@qmul.ac.uk)#TAB#","institution_ids":["https://openalex.org/I166337079"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035765654","display_name":"Klas Markstr\u00f6m","orcid":"https://orcid.org/0000-0002-6344-1642"},"institutions":[{"id":"https://openalex.org/I90267481","display_name":"Ume\u00e5 University","ror":"https://ror.org/05kb8h459","country_code":"SE","type":"education","lineage":["https://openalex.org/I90267481"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"KLAS MARKSTR\u00d6M","raw_affiliation_strings":["Department of Mathematics and Mathematical Statistics, Ume\u00e5 University, Ume\u00e5 901 87, Sweden (e-mail:","Department of mathematics and mathematical statistics, ume\u00e5 university, ume\u00e5 901 87, sweden e-mail: klas.markstrom@math.umu.se#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Mathematical Statistics, Ume\u00e5 University, Ume\u00e5 901 87, Sweden (e-mail:","institution_ids":["https://openalex.org/I90267481"]},{"raw_affiliation_string":"Department of mathematics and mathematical statistics, ume\u00e5 university, ume\u00e5 901 87, sweden e-mail: klas.markstrom@math.umu.se#TAB#","institution_ids":["https://openalex.org/I90267481"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":1.785,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.83981233,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"22","issue":"1","first_page":"55","last_page":"70"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9987999796867371,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.8985066413879395},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6816998720169067},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.5896875262260437},{"id":"https://openalex.org/keywords/intersection-graph","display_name":"Intersection graph","score":0.5552107691764832},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5187616348266602},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5088555812835693},{"id":"https://openalex.org/keywords/ramseys-theorem","display_name":"Ramsey's theorem","score":0.47867876291275024},{"id":"https://openalex.org/keywords/ramsey-theory","display_name":"Ramsey theory","score":0.4657403230667114},{"id":"https://openalex.org/keywords/family-of-sets","display_name":"Family of sets","score":0.44756263494491577},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.44238170981407166},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41817545890808105},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.27525585889816284},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.11413928866386414},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10193058848381042}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8985066413879395},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6816998720169067},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5896875262260437},{"id":"https://openalex.org/C54540088","wikidata":"https://www.wikidata.org/wiki/Q3498041","display_name":"Intersection graph","level":4,"score":0.5552107691764832},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5187616348266602},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5088555812835693},{"id":"https://openalex.org/C44115641","wikidata":"https://www.wikidata.org/wiki/Q918099","display_name":"Ramsey's theorem","level":3,"score":0.47867876291275024},{"id":"https://openalex.org/C112291201","wikidata":"https://www.wikidata.org/wiki/Q1336170","display_name":"Ramsey theory","level":2,"score":0.4657403230667114},{"id":"https://openalex.org/C150591576","wikidata":"https://www.wikidata.org/wiki/Q739925","display_name":"Family of sets","level":3,"score":0.44756263494491577},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.44238170981407166},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41817545890808105},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.27525585889816284},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.11413928866386414},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10193058848381042},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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":2,"locations":[{"id":"doi:10.1017/s0963548312000429","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548312000429","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.714.5204","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.714.5204","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://abel.math.umu.se/%7Eklasm/Uppsatser/cubeint.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W112858196","https://openalex.org/W1508622653","https://openalex.org/W1954214817","https://openalex.org/W1984324531","https://openalex.org/W1989755735","https://openalex.org/W2004308928","https://openalex.org/W2011575706","https://openalex.org/W2014178973","https://openalex.org/W2051336598","https://openalex.org/W2074920973","https://openalex.org/W2088622619","https://openalex.org/W2100437838","https://openalex.org/W2115730400","https://openalex.org/W2133795933","https://openalex.org/W2152486369","https://openalex.org/W2165064763","https://openalex.org/W2166750439","https://openalex.org/W2321467776","https://openalex.org/W2798428635","https://openalex.org/W3104768492","https://openalex.org/W4237496336"],"related_works":["https://openalex.org/W13791998","https://openalex.org/W2474561564","https://openalex.org/W2949231378","https://openalex.org/W4301914467","https://openalex.org/W2127133075","https://openalex.org/W2950410478","https://openalex.org/W4301765976","https://openalex.org/W4297817664","https://openalex.org/W2292548913","https://openalex.org/W2091690195"],"abstract_inverted_index":{"The":[0,116,240,251],"discrete":[1,50],"cube":[2],"{0,":[3,13,164],"1}d":[4,14],"is":[5,15,40,190,224,229,290],"a":[6,16,62,120,181,191,248],"fundamental":[7],"combinatorial":[8],"structure.":[9],"A":[10],"subcube":[11],"of":[12,18,20,44,48,64,72,119,122,148,161,178,202,237,246],"subset":[17],"2k":[19],"its":[21],"points":[22],"formed":[23],"by":[24],"fixing":[25],"k":[26,34,96,216],"coordinates":[27],"and":[28,101,204,292],"allowing":[29],"the":[30,49,131,139,146,158,175,220,234,238,259,263,286,297],"remaining":[31],"d":[32],"\u2212":[33],"to":[35,233],"vary":[36],"freely.":[37],"This":[38],"paper":[39],"concerned":[41],"with":[42,133,296],"patterns":[43],"intersections":[45,80],"among":[46,91],"subcubes":[47,65,86,162],"cube.":[51],"Two":[52],"sample":[53],"questions":[54,109],"along":[55],"these":[56],"lines":[57],"are":[58,94,105,110,272],"as":[59,157,247,262],"follows:":[60],"given":[61],"family":[63,121,132],"in":[66,130,163,180,184,258,273],"which":[67,97,104,153,271],"no":[68,95,102],"r":[69,203],"+":[70],"1":[71],"them":[73,92],"have":[74,89,98],"non-empty":[75,99],"intersection,":[76],"how":[77],"many":[78,85],"pairwise":[79,106],"can":[81,87,154,243,255],"we":[82,88,208],"have?":[83],"How":[84],"if":[90,138,211],"there":[93],"intersection":[100,114,117,159],"l":[103,289],"disjoint?":[107],"These":[108],"naturally":[111],"expressed":[112],"using":[113],"graphs.":[115],"graph":[118,183],"sets":[123],"has":[124],"one":[125],"vertex":[126,151],"for":[127,174,199,213,279],"each":[128],"set":[129,147],"two":[134],"vertices":[135],"being":[136],"adjacent":[137],"corresponding":[140],"subsets":[141],"intersect.":[142],"Let":[143],"$\\I(n,d)$":[144,185,274],"be":[145,155,244,256],"all":[149],"n":[150,228,254,282],"graphs":[152,160,270],"represented":[156],"1}d.":[165],"With":[166],"this":[167,196,280],"notation":[168],"our":[169],"first":[170],"question":[171,197,242],"above":[172],"asks":[173],"largest":[176],"number":[177,266],"edges":[179],"Kr+1-free":[182],".":[186,275],"As":[187],"such":[188,253],"it":[189],"Tur\u00e1n-type":[192],"problem.":[193,250],"We":[194,276],"answer":[195],"asymptotically":[198],"some":[200,214,294],"ranges":[201],"d.":[205],"More":[206],"precisely":[207],"show":[209],"that":[210,227,288],"$(k+1)2^{\\lfloor\\frac{d}{k+1}\\rfloor}":[212],"integer":[215],"\u2265":[217],"2":[218],"then":[219],"maximum":[221,252,281],"edge":[222],"density":[223],"$\\bigl(1-\\frac{1}{k}-o(1)\\bigr)$":[225],"provided":[226],"not":[230],"too":[231],"close":[232],"lower":[235],"limit":[236],"range.":[239],"second":[241],"thought":[245],"Ramsey-type":[249],"defined":[257],"same":[260],"way":[261],"usual":[264,298],"Ramsey":[265,299],"but":[267],"only":[268],"considering":[269],"give":[277],"bounds":[278],"mainly":[283],"concentrating":[284],"on":[285],"case":[287],"fixed,":[291],"make":[293],"comparisons":[295],"number.":[300]},"counts_by_year":[{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}