{"id":"https://openalex.org/W2804545386","doi":"https://doi.org/10.37236/7885","title":"On Resilience of Connectivity in the Evolution of Random Graphs","display_name":"On Resilience of Connectivity in the Evolution of Random Graphs","publication_year":2019,"publication_date":"2019-05-17","ids":{"openalex":"https://openalex.org/W2804545386","doi":"https://doi.org/10.37236/7885","mag":"2804545386"},"language":"en","primary_location":{"id":"doi:10.37236/7885","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7885","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p24/7837","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p24/7837","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039056700","display_name":"Luc Haller","orcid":null},"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"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Luc Haller","raw_affiliation_strings":["ETH Z\u00fcrich"],"affiliations":[{"raw_affiliation_string":"ETH Z\u00fcrich","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033615437","display_name":"Milo\u0161 Truji\u0107","orcid":"https://orcid.org/0000-0002-7592-3630"},"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"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Milo\u0161 Truji\u0107","raw_affiliation_strings":["ETH Z\u00fcrich"],"affiliations":[{"raw_affiliation_string":"ETH Z\u00fcrich","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039056700"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06132226,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":"2","first_page":null,"last_page":null},"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":0.9991999864578247,"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":0.9991999864578247,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9976000189781189,"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":0.9958000183105469,"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":0.8009575605392456},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6418330669403076},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.6358535289764404},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6184366345405579},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5959395170211792},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4134776294231415},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08005136251449585}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8009575605392456},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6418330669403076},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.6358535289764404},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6184366345405579},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5959395170211792},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4134776294231415},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08005136251449585}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.37236/7885","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7885","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p24/7837","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:research-collection.ethz.ch:20.500.11850/345303","is_oa":false,"landing_page_url":"http://hdl.handle.net/20.500.11850/345303","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics, 26 (2)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1805.08744","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1805.08744","pdf_url":"https://arxiv.org/pdf/1805.08744","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.1805.08744","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1805.08744","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"article"},{"id":"doi:10.3929/ethz-b-000345303","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000345303","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","issn_l":null,"issn":[],"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":"article-journal"},{"id":"mag:2804545386","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.37236/7885","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7885","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p24/7837","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1305807678","display_name":"Extreme Value Theory as a Tool for Financial Risk Management.","funder_award_id":"69242","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G4836148144","display_name":null,"funder_award_id":"20002","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G7913294716","display_name":null,"funder_award_id":"200021 169242","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G907367802","display_name":null,"funder_award_id":"169242","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G993971353","display_name":null,"funder_award_id":"200021","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2804545386.pdf","grobid_xml":"https://content.openalex.org/works/W2804545386.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1489878404","https://openalex.org/W1504514920","https://openalex.org/W1639593279","https://openalex.org/W1971367602","https://openalex.org/W1976052016","https://openalex.org/W1988476087","https://openalex.org/W1991646384","https://openalex.org/W2020233469","https://openalex.org/W2030651378","https://openalex.org/W2048267719","https://openalex.org/W2072508453","https://openalex.org/W2075689026","https://openalex.org/W2097823813","https://openalex.org/W2126648306","https://openalex.org/W2146162554","https://openalex.org/W2336317531","https://openalex.org/W2529837827","https://openalex.org/W2588221380","https://openalex.org/W2611093227","https://openalex.org/W2755146433","https://openalex.org/W2761339831","https://openalex.org/W2761589359","https://openalex.org/W2765360845","https://openalex.org/W2905110430","https://openalex.org/W2963201929","https://openalex.org/W2964065454","https://openalex.org/W3020946092"],"related_works":["https://openalex.org/W2962848126","https://openalex.org/W848155213","https://openalex.org/W2950511270","https://openalex.org/W2033124856","https://openalex.org/W2964081956","https://openalex.org/W3158280387","https://openalex.org/W2978072813","https://openalex.org/W2042833774","https://openalex.org/W1966703244","https://openalex.org/W2950813788","https://openalex.org/W3040465303","https://openalex.org/W1857266183","https://openalex.org/W3001133135","https://openalex.org/W2245679762","https://openalex.org/W2002045419","https://openalex.org/W3081036497","https://openalex.org/W2952877998","https://openalex.org/W1977037817","https://openalex.org/W3102409779","https://openalex.org/W3112610719"],"abstract_inverted_index":{"In":[0],"this":[1],"note":[2],"we":[3],"establish":[4],"a":[5,31,72],"resilience":[6,166],"version":[7],"of":[8,14,136,160],"the":[9,55,66,99,105,113,132,151,154,158,165],"classical":[10],"hitting":[11],"time":[12],"result":[13,147],"Bollob\u00e1s":[15],"and":[16,102,162],"Thomason":[17],"regarding":[18],"connectivity.":[19,145],"A":[20],"graph":[21,34,56,68,79,106,115],"$G$":[22],"is":[23,71,93,117,138,148],"said":[24],"to":[25,30,104,144],"be":[26,65,168],"$\\alpha$-resilient":[27],"with":[28,76,142],"respect":[29,143],"monotone":[32],"increasing":[33],"property":[35],"$\\mathcal{P}$":[36],"if":[37],"for":[38,50,175],"every":[39],"spanning":[40],"subgraph":[41],"$H":[42],"\\subseteq":[43],"G$":[44],"satisfying":[45],"$\\deg_H(v)":[46],"\\leqslant":[47],"\\alpha":[48],"\\deg_G(v)$":[49],"all":[51],"$v":[52],"\\in":[53],"V(G)$,":[54],"$G":[57],"-":[58,108,140],"H$":[59],"still":[60],"possesses":[61],"$\\mathcal{P}$.":[62],"Let":[63],"$\\{G_i\\}$":[64],"random":[67,97,114],"process,":[69],"that":[70,112,121,153],"process":[73,116],"where,":[74],"starting":[75,122],"an":[77,90],"empty":[78],"on":[80],"$n$":[81],"vertices":[82],"$G_0$,":[83],"in":[84,150,157,164],"each":[85],"step":[86],"$i":[87],"\\geqslant":[88,125],"1$":[89],"edge":[91],"$e$":[92],"chosen":[94],"uniformly":[95],"at":[96],"among":[98],"missing":[100],"ones":[101],"added":[103],"$G_{i":[107],"1}$.":[109],"We":[110,171],"show":[111],"almost":[118],"surely":[119],"such":[120],"from":[123],"$m":[124],"(\\tfrac{1}{6}":[126],"+":[127],"o(1))":[128],"n":[129],"\\log":[130],"n$,":[131],"largest":[133],"connected":[134],"component":[135],"$G_m$":[137],"$(\\tfrac{1}{2}":[139],"o(1))$-resilient":[141],"The":[146],"optimal":[149],"sense":[152],"constants":[155],"$1/6$":[156],"number":[159],"edges":[161],"$1/2$":[163],"cannot":[167],"improved":[169],"upon.":[170],"obtain":[172],"similar":[173],"results":[174],"$k$-connectivity.":[176]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}