{"id":"https://openalex.org/W2072859770","doi":"https://doi.org/10.1017/s096354831000026x","title":"Pegging Graphs Yields a Small Diameter","display_name":"Pegging Graphs Yields a Small Diameter","publication_year":2010,"publication_date":"2010-08-24","ids":{"openalex":"https://openalex.org/W2072859770","doi":"https://doi.org/10.1017/s096354831000026x","mag":"2072859770"},"language":"en","primary_location":{"id":"doi:10.1017/s096354831000026x","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s096354831000026x","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/CA5AAEB63EDA14475B72772AD9F84C19/S096354831000026Xa.pdf/div-class-title-pegging-graphs-yields-a-small-diameter-div.pdf","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","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/CA5AAEB63EDA14475B72772AD9F84C19/S096354831000026Xa.pdf/div-class-title-pegging-graphs-yields-a-small-diameter-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047303000","display_name":"Stefanie Gerke","orcid":"https://orcid.org/0000-0002-9426-1708"},"institutions":[{"id":"https://openalex.org/I184558857","display_name":"Royal Holloway University of London","ror":"https://ror.org/04g2vpn86","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I184558857"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"STEFANIE GERKE","raw_affiliation_strings":["Mathematics Department, Royal Holloway College, University of London, Egham, TW20 0EX, UK (e-mail:","Mathematics department, royal holloway college, university of london, egham, tw20 0ex, uk (e-mail: stefanie.gerke@rhul.ac.uk)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, Royal Holloway College, University of London, Egham, TW20 0EX, UK (e-mail:","institution_ids":["https://openalex.org/I184558857"]},{"raw_affiliation_string":"Mathematics department, royal holloway college, university of london, egham, tw20 0ex, uk (e-mail: stefanie.gerke@rhul.ac.uk)","institution_ids":["https://openalex.org/I184558857"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062687538","display_name":"Angelika Steger","orcid":"https://orcid.org/0000-0002-3465-3996"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]},{"id":"https://openalex.org/I4210090941","display_name":"Institute for Biomedical Engineering","ror":"https://ror.org/00baskk38","country_code":"CH","type":"facility","lineage":["https://openalex.org/I202697423","https://openalex.org/I2799323385","https://openalex.org/I35440088","https://openalex.org/I4210090941"]},{"id":"https://openalex.org/I4210112966","display_name":"Instituto de F\u00edsica Te\u00f3rica","ror":"https://ror.org/022r8mj40","country_code":"ES","type":"facility","lineage":["https://openalex.org/I134820265","https://openalex.org/I4210112966","https://openalex.org/I63634437"]}],"countries":["CH","ES"],"is_corresponding":false,"raw_author_name":"ANGELIKA STEGER","raw_affiliation_strings":["Institute for Theoretical Computer Science, ETH Zurich, CH-8092 Zurich, Switzerland (e-mail:","Institute for theoretical computer science, eth zurich, ch-8092 zurich, switzerland (e-mail: steger@inf.ethz.ch)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Computer Science, ETH Zurich, CH-8092 Zurich, Switzerland (e-mail:","institution_ids":["https://openalex.org/I35440088","https://openalex.org/I4210090941","https://openalex.org/I4210112966"]},{"raw_affiliation_string":"Institute for theoretical computer science, eth zurich, ch-8092 zurich, switzerland (e-mail: steger@inf.ethz.ch)#TAB#","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113900323","display_name":"Nicholas Wormald","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"NICHOLAS WORMALD","raw_affiliation_strings":["Department of Combinatorics and Optimization, University of Waterloo, Waterloo ON, N2L 3G1, Canada (e-mail:","Department of combinatorics and optimization, university of waterloo, waterloo on, n2l 3g1, canada (e-mail: nwormald@uwaterloo.ca)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Combinatorics and Optimization, University of Waterloo, Waterloo ON, N2L 3G1, Canada (e-mail:","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of combinatorics and optimization, university of waterloo, waterloo on, n2l 3g1, canada (e-mail: nwormald@uwaterloo.ca)","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.14617242,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"20","issue":"2","first_page":"239","last_page":"248"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9987999796867371,"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":0.9987999796867371,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9958999752998352,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9955999851226807,"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/logarithm","display_name":"Logarithm","score":0.7524588704109192},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5496611595153809},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5387389063835144},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.531414806842804},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5115324258804321},{"id":"https://openalex.org/keywords/random-regular-graph","display_name":"Random regular graph","score":0.4671909809112549},{"id":"https://openalex.org/keywords/midpoint","display_name":"Midpoint","score":0.44349732995033264},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.4187781512737274},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41087424755096436},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.3952629566192627},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.3141491711139679},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15007320046424866},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05411320924758911}],"concepts":[{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.7524588704109192},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5496611595153809},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5387389063835144},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.531414806842804},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5115324258804321},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.4671909809112549},{"id":"https://openalex.org/C34130140","wikidata":"https://www.wikidata.org/wiki/Q1645406","display_name":"Midpoint","level":2,"score":0.44349732995033264},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.4187781512737274},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41087424755096436},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.3952629566192627},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.3141491711139679},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15007320046424866},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05411320924758911}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1017/s096354831000026x","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s096354831000026x","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/CA5AAEB63EDA14475B72772AD9F84C19/S096354831000026Xa.pdf/div-class-title-pegging-graphs-yields-a-small-diameter-div.pdf","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:research-collection.ethz.ch:20.500.11850/30822","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/30822","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability & Computing, 20 (2)","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doc.rero.ch:298667","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400148","display_name":"reroDoc Digital Library","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"doi:10.3929/ethz-b-000030822","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000030822","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Other"}],"best_oa_location":{"id":"doi:10.1017/s096354831000026x","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s096354831000026x","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/CA5AAEB63EDA14475B72772AD9F84C19/S096354831000026Xa.pdf/div-class-title-pegging-graphs-yields-a-small-diameter-div.pdf","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2072859770.pdf","grobid_xml":"https://content.openalex.org/works/W2072859770.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W5090298","https://openalex.org/W1570131048","https://openalex.org/W1592213313","https://openalex.org/W1981927600","https://openalex.org/W2013493321","https://openalex.org/W2040232420","https://openalex.org/W2046441507","https://openalex.org/W2100158662","https://openalex.org/W2151221105","https://openalex.org/W3017336888","https://openalex.org/W3083259271"],"related_works":["https://openalex.org/W2963631220","https://openalex.org/W4301442952","https://openalex.org/W2143498657","https://openalex.org/W3002604364","https://openalex.org/W2138204011","https://openalex.org/W87964322","https://openalex.org/W3083738242","https://openalex.org/W2050262222","https://openalex.org/W2195927477","https://openalex.org/W2072859770"],"abstract_inverted_index":{"We":[0,28],"consider":[1],"the":[2,21,31],"following":[3],"process":[4,41],"for":[5],"generating":[6],"large":[7],"random":[8],"cubic":[9],"graphs.":[10],"Starting":[11],"with":[12],"a":[13,45],"given":[14],"graph,":[15],"repeatedly":[16],"add":[17],"edges":[18],"that":[19,30,57],"join":[20],"midpoints":[22],"of":[23,48,61],"two":[24],"randomly":[25],"chosen":[26],"edges.":[27],"show":[29],"growing":[32],"graph":[33],"asymptotically":[34],"almost":[35],"surely":[36],"has":[37],"logarithmic":[38],"diameter.":[39],"This":[40],"is":[42],"motivated":[43],"by":[44],"particular":[46],"type":[47],"peer-to-peer":[49],"network.":[50],"Our":[51],"method":[52],"extends":[53],"to":[54],"similar":[55],"processes":[56],"generate":[58],"regular":[59],"graphs":[60],"higher":[62],"degree.":[63]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}