{"id":"https://openalex.org/W2107412034","doi":"https://doi.org/10.1017/s0963548310000040","title":"Decompositions into Subgraphs of Small Diameter","display_name":"Decompositions into Subgraphs of Small Diameter","publication_year":2010,"publication_date":"2010-06-09","ids":{"openalex":"https://openalex.org/W2107412034","doi":"https://doi.org/10.1017/s0963548310000040","mag":"2107412034"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548310000040","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548310000040","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/A5112361944","display_name":"Jacob Fox","orcid":"https://orcid.org/0000-0002-0664-497X"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"JACOB FOX","raw_affiliation_strings":["Department of Mathematics, Princeton, Princeton, NJ, USA (e-mail:","Department of mathematics, princeton, princeton, nj, usa (e-mail: jacobfox@math.princeton.edu)#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Princeton, Princeton, NJ, USA (e-mail:","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Department of mathematics, princeton, princeton, nj, usa (e-mail: jacobfox@math.princeton.edu)#TAB#","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066741544","display_name":"Benny Sudakov","orcid":"https://orcid.org/0000-0003-3307-9475"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"BENNY SUDAKOV","raw_affiliation_strings":["Department of Mathematics, UCLA, Los Angeles, CA 90095, USA (e-mail:","Department of mathematics, ucla, los angeles, ca 90095, usa (e-mail: bsudakov@math.ucla.edu)#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, UCLA, Los Angeles, CA 90095, USA (e-mail:","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Department of mathematics, ucla, los angeles, ca 90095, usa (e-mail: bsudakov@math.ucla.edu)#TAB#","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112361944"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":0.9501,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.72289157,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"19","issue":"5-6","first_page":"753","last_page":"774"},"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":0.9997000098228455,"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":0.9961000084877014,"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/combinatorics","display_name":"Combinatorics","score":0.875246524810791},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7185754776000977},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5858017802238464},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5852245092391968},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5189982652664185},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.47877633571624756},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.45754143595695496},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3832857608795166},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07050248980522156},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.04947161674499512}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.875246524810791},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7185754776000977},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5858017802238464},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5852245092391968},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5189982652664185},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.47877633571624756},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.45754143595695496},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3832857608795166},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07050248980522156},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.04947161674499512},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"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:10.1017/s0963548310000040","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548310000040","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W111038805","https://openalex.org/W619755549","https://openalex.org/W1975473448","https://openalex.org/W1998544343","https://openalex.org/W2003995429","https://openalex.org/W2014447809","https://openalex.org/W2021989224","https://openalex.org/W2029361670","https://openalex.org/W2063190536","https://openalex.org/W2081231159","https://openalex.org/W2082945930","https://openalex.org/W2115730400","https://openalex.org/W2146592359","https://openalex.org/W4245766261","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3006682748","https://openalex.org/W1097487277","https://openalex.org/W2768610039","https://openalex.org/W4308265086","https://openalex.org/W2949964783","https://openalex.org/W4285390085","https://openalex.org/W2801357573","https://openalex.org/W2974000959","https://openalex.org/W2106889256","https://openalex.org/W2982363256"],"abstract_inverted_index":{"We":[0,203],"investigate":[1],"decompositions":[2],"of":[3,10,76,126,216,225,232,240],"a":[4,7,107,123,131,222],"graph":[5,28,118],"into":[6,122],"small":[8,124,223],"number":[9,125,224],"low-diameter":[11,226],"subgraphs.":[12,227],"Let":[13],"P":[14,97,143,157,173,189],"(":[15,31,98,144,158,174,190],"n":[16,37,63,99,145,159,165,175,186,191,200],",":[17,33,65,100,146,160,176,192],"\u03b5,":[18,101,147,161,177,193],"d":[19,86,148],")":[20,35,149,166,182],"be":[21,120,135,219],"the":[22,74,77,214],"smallest":[23],"k":[24,54,73],"such":[25,55],"that":[26,56,96,115,130,156,206],"every":[27,116],"G":[29,208,217],"=":[30,44,163,179,195],"V":[32],"E":[34,43,45,48,53,58,81],"on":[36,111,138],"vertices":[38],"has":[39,209],"an":[40,151],"edge":[41],"partition":[42],"0":[46,59],"\u222a":[47,50,52],"1":[49,69],"\u22c5\u22c5\u22c5":[51],"|":[57,60],"\u2264":[61,70,72],"\u03b5":[62,170,184,198],"2":[64,181],"and":[66,93,188,244],"for":[67,169,183,197],"all":[68,213],"i":[71,82],"diameter":[75],"subgraph":[78],"spanned":[79],"by":[80,106,221],"is":[83,103,167],"at":[84],"most":[85],".":[87,202],"Using":[88],"Szemer\u00e9di's":[89],"regularity":[90],"lemma,":[91],"Polcyn":[92],"Ruci\u0144ski":[94,243],"showed":[95],"4)":[102,194],"bounded":[104],"above":[105],"constant":[108,153],"depending":[109],"only":[110],"\u03b5.":[112],"This":[113],"shows":[114],"dense":[117],"can":[119,134,218],"partitioned":[121],"\u2018small":[127],"worlds\u2019":[128],"provided":[129],"few":[132],"edges":[133,215],"ignored.":[136],"Improving":[137],"their":[139],"result,":[140],"we":[141,229],"determine":[142],"within":[150],"absolute":[152],"factor,":[154],"showing":[155],"2)":[162],"\u0398(":[164],"unbounded":[168],"&lt;":[171],"1/4,":[172],"3)":[178],"\u0398(1/\u03b5":[180],"&gt;":[185,199],"\u22121/2":[187],"\u0398(1/\u03b5)":[196],"\u22121":[201],"also":[204],"prove":[205],"if":[207],"large":[210],"minimum":[211],"degree,":[212],"covered":[220],"Finally,":[228],"extend":[230],"some":[231],"these":[233],"results":[234],"to":[235],"hypergraphs,":[236],"improving":[237],"earlier":[238],"work":[239],"Polcyn,":[241],"R\u00f6dl,":[242],"Szemer\u00e9di.":[245]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
