{"id":"https://openalex.org/W4393934586","doi":"https://doi.org/10.1007/s00493-024-00089-0","title":"Isoperimetric Inequalities and Supercritical Percolation on High-Dimensional Graphs","display_name":"Isoperimetric Inequalities and Supercritical Percolation on High-Dimensional Graphs","publication_year":2024,"publication_date":"2024-04-04","ids":{"openalex":"https://openalex.org/W4393934586","doi":"https://doi.org/10.1007/s00493-024-00089-0"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-024-00089-0","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00493-024-00089-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-024-00089-0.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00493-024-00089-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081714572","display_name":"Sahar Diskin","orcid":"https://orcid.org/0000-0002-5586-8152"},"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"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Sahar Diskin","raw_affiliation_strings":["School of Mathematical Sciences, Tel Aviv University, 6997801, Tel Aviv, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Tel Aviv University, 6997801, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028299034","display_name":"Joshua Erde","orcid":"https://orcid.org/0000-0003-1129-4270"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Joshua Erde","raw_affiliation_strings":["Institute of Discrete Mathematics, Graz University of Technology, Steyrergasse 30, 8010, Graz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Discrete Mathematics, Graz University of Technology, Steyrergasse 30, 8010, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002103922","display_name":"Mihyun Kang","orcid":"https://orcid.org/0000-0001-8729-2779"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Mihyun Kang","raw_affiliation_strings":["Institute of Discrete Mathematics, Graz University of Technology, Steyrergasse 30, 8010, Graz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Discrete Mathematics, Graz University of Technology, Steyrergasse 30, 8010, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008556299","display_name":"Michael Krivelevich","orcid":"https://orcid.org/0000-0003-2357-4982"},"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"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Michael Krivelevich","raw_affiliation_strings":["School of Mathematical Sciences, Tel Aviv University, 6997801, Tel Aviv, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Tel Aviv University, 6997801, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5081714572"],"corresponding_institution_ids":["https://openalex.org/I16391192"],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":{"value":3190,"currency":"USD","value_usd":3190},"fwci":1.3923,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.74501151,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"44","issue":"4","first_page":"741","last_page":"784"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9988999962806702,"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/T11476","display_name":"Graph theory and applications","score":0.9980999827384949,"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/isoperimetric-inequality","display_name":"Isoperimetric inequality","score":0.9408255815505981},{"id":"https://openalex.org/keywords/supercritical-fluid","display_name":"Supercritical fluid","score":0.7133239507675171},{"id":"https://openalex.org/keywords/percolation","display_name":"Percolation (cognitive psychology)","score":0.5954629182815552},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4842912554740906},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.45545855164527893},{"id":"https://openalex.org/keywords/isoperimetric-dimension","display_name":"Isoperimetric dimension","score":0.44206130504608154},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.395885705947876},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25467315316200256},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13229107856750488},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.13091161847114563},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.0760807991027832}],"concepts":[{"id":"https://openalex.org/C140142295","wikidata":"https://www.wikidata.org/wiki/Q617417","display_name":"Isoperimetric inequality","level":2,"score":0.9408255815505981},{"id":"https://openalex.org/C118419359","wikidata":"https://www.wikidata.org/wiki/Q682585","display_name":"Supercritical fluid","level":2,"score":0.7133239507675171},{"id":"https://openalex.org/C2780457167","wikidata":"https://www.wikidata.org/wiki/Q17156484","display_name":"Percolation (cognitive psychology)","level":2,"score":0.5954629182815552},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4842912554740906},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.45545855164527893},{"id":"https://openalex.org/C70266181","wikidata":"https://www.wikidata.org/wiki/Q3707726","display_name":"Isoperimetric dimension","level":3,"score":0.44206130504608154},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.395885705947876},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25467315316200256},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13229107856750488},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.13091161847114563},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0760807991027832},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00493-024-00089-0","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00493-024-00089-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-024-00089-0.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:openaire/4e252398-e0e7-45dc-9f68-cb37ce05bbf3","is_oa":true,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/4e252398-e0e7-45dc-9f68-cb37ce05bbf3","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Diskin, S, Erde, J, Kang, M & Krivelevich, M 2024, 'Isoperimetric Inequalities and Supercritical Percolation on High-Dimensional Graphs', Combinatorica, vol. 44, no. 4, pp. 741-784. https://doi.org/10.1007/s00493-024-00089-0","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1007/s00493-024-00089-0","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00493-024-00089-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-024-00089-0.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6196800289","display_name":"Discrete Mathematics","funder_award_id":"W 1230","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320322596","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4393934586.pdf","grobid_xml":"https://content.openalex.org/works/W4393934586.grobid-xml"},"referenced_works_count":53,"referenced_works":["https://openalex.org/W100944330","https://openalex.org/W593649846","https://openalex.org/W1488446430","https://openalex.org/W1505597232","https://openalex.org/W1610677200","https://openalex.org/W1637337126","https://openalex.org/W1964574310","https://openalex.org/W1965062900","https://openalex.org/W1977850459","https://openalex.org/W1993111701","https://openalex.org/W1993216347","https://openalex.org/W1998236864","https://openalex.org/W1998400388","https://openalex.org/W2000630284","https://openalex.org/W2001735302","https://openalex.org/W2010025177","https://openalex.org/W2012335152","https://openalex.org/W2013770427","https://openalex.org/W2017052287","https://openalex.org/W2018047324","https://openalex.org/W2022912148","https://openalex.org/W2026620883","https://openalex.org/W2032950184","https://openalex.org/W2043819676","https://openalex.org/W2044881936","https://openalex.org/W2063054346","https://openalex.org/W2075997628","https://openalex.org/W2077562249","https://openalex.org/W2081052144","https://openalex.org/W2089498317","https://openalex.org/W2093126960","https://openalex.org/W2098298439","https://openalex.org/W2158059367","https://openalex.org/W2167405849","https://openalex.org/W2259634959","https://openalex.org/W2318698654","https://openalex.org/W2336317531","https://openalex.org/W2604607828","https://openalex.org/W2769174420","https://openalex.org/W2885549115","https://openalex.org/W2907316818","https://openalex.org/W2949544577","https://openalex.org/W2950850272","https://openalex.org/W2964026298","https://openalex.org/W3100974711","https://openalex.org/W3103572255","https://openalex.org/W3211981972","https://openalex.org/W4238443289","https://openalex.org/W4247423216","https://openalex.org/W4249774010","https://openalex.org/W4250226066","https://openalex.org/W4302344174","https://openalex.org/W4390013332"],"related_works":["https://openalex.org/W4288108205","https://openalex.org/W2003619291","https://openalex.org/W2317142650","https://openalex.org/W2972486114","https://openalex.org/W2049220294","https://openalex.org/W2009681213","https://openalex.org/W4289025481","https://openalex.org/W4297812615","https://openalex.org/W2092426748","https://openalex.org/W2382975176"],"abstract_inverted_index":{"Abstract":[0],"It":[1],"is":[2,137,150],"known":[3,285,310],"that":[4,41,123,157,178],"many":[5],"different":[6],"types":[7],"of":[8,25,32,51,83,96,109,140,231,242,258,261,290,303],"finite":[9],"random":[10,245],"subgraph":[11,186],"models":[12],"undergo":[13],"quantitatively":[14],"similar":[15],"phase":[16,44],"transitions":[17],"around":[18],"their":[19],"percolation":[20,118],"thresholds,":[21],"and":[22,88,144,299],"the":[23,33,38,61,79,86,107,110,138,141,207,228,238,255,284,288,291,296],"proofs":[24],"these":[26,102,120,214],"results":[27,201,275],"rely":[28],"on":[29,119,247],"isoperimetric":[30,69,81,103],"properties":[31,104],"underlying":[34],"host":[35],"graph.":[36],"Recently,":[37],"authors":[39],"showed":[40],"such":[42,72],"a":[43,48,57,93,151,184,243,259],"transition":[45],"occurs":[46],"in":[47,116,210,225,287,294,314],"large":[49],"class":[50],"regular":[52,73],"high-dimensional":[53,74],"product":[54,75,121,142],"graphs,":[55,76,122],"generalising":[56],"classic":[58],"result":[59],"for":[60,71,85,92],"hypercube.":[62],"In":[63],"this":[64],"paper":[65],"we":[66,176,218,253],"give":[67],"new":[68],"inequalities":[70],"which":[77],"generalise":[78],"well-known":[80],"inequality":[82],"Harper":[84],"hypercube,":[87,292],"are":[89,202],"asymptotically":[90],"sharp":[91],"wide":[94],"range":[95],"set":[97],"sizes.":[98],"We":[99,155],"then":[100],"use":[101],"to":[105,206,221,311],"investigate":[106],"structure":[108],"giant":[111],"component":[112],"$$L_1$$":[113,159,179,232,248,304],"L":[114,160,180,233,249,305],"1":[115,130,161,170,181,195,234,250,306],"supercritical":[117],"is,":[124],"when":[125],"$$p=\\frac{1+\\epsilon":[126],"}{d}$$":[127],"p":[128],"=":[129],"+":[131],"\u03f5":[132,147],"d":[133,136,171,173,196,198,211,226,270,272,315],",":[134,227],"where":[135,293],"degree":[139],"graph":[143],"$$\\epsilon":[145],">0$$":[146],">":[148],"0":[149],"small":[152,222],"enough":[153],"constant.":[154],"show":[156,177,254],"typically":[158],"has":[162],"edge-expansion":[163],"$$\\Omega":[164,189,263],"\\left(":[165,190,264],"\\frac{1}{d\\ln":[166,191],"d}\\right)":[167,192,266],"$$":[168,193,267],"\u03a9":[169,194,268],"ln":[172,197,271],".":[174,199,212,251,273,316],"Furthermore,":[175,252],"likely":[182,215,229,256,297],"contains":[183],"linear-sized":[185],"with":[187],"vertex-expansion":[188],"These":[200,274],"best":[203],"possible":[204],"up":[205,220],"logarithmic":[208],"factor":[209],"Using":[213],"expansion":[216],"properties,":[217],"determine,":[219],"polylogarithmic":[223],"factors":[224],"diameter":[230,298],"as":[235,237],"well":[236],"typical":[239,300],"mixing":[240,301],"time":[241,302],"lazy":[244],"walk":[246],"existence":[257],"cycle":[260],"length":[262],"\\frac{n}{d\\ln":[265],"n":[269],"not":[276],"only":[277,309],"generalise,":[278],"but":[279],"also":[280],"improve":[281],"substantially":[282],"upon":[283],"bounds":[286],"case":[289],"particular":[295],"were":[307],"previously":[308],"be":[312],"polynomial":[313]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}