{"id":"https://openalex.org/W1904326042","doi":"https://doi.org/10.1017/s0963548316000377","title":"Saturated Graphs of Prescribed Minimum Degree","display_name":"Saturated Graphs of Prescribed Minimum Degree","publication_year":2016,"publication_date":"2016-12-07","ids":{"openalex":"https://openalex.org/W1904326042","doi":"https://doi.org/10.1017/s0963548316000377","mag":"1904326042"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548316000377","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548316000377","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A1FC8D7941DF0B67A3BA4DF9F90DE6B4/S0963548316000377a.pdf/div-class-title-saturated-graphs-of-prescribed-minimum-degree-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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A1FC8D7941DF0B67A3BA4DF9F90DE6B4/S0963548316000377a.pdf/div-class-title-saturated-graphs-of-prescribed-minimum-degree-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"A. NICHOLAS DAY","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":true,"raw_author_name":"A. NICHOLAS DAY","raw_affiliation_strings":["School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK (e-mail:"],"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"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I166337079"],"apc_list":null,"apc_paid":null,"fwci":1.3272,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.75681391,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"26","issue":"2","first_page":"201","last_page":"207"},"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":0.7670999765396118,"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":0.7670999765396118,"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":0.07129999995231628,"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"}},{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.057100001722574234,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/conjecture","display_name":"Conjecture","score":0.555400013923645},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5414999723434448},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5324000120162964},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.42899999022483826},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.3977000117301941},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.3698999881744385},{"id":"https://openalex.org/keywords/induced-subgraph","display_name":"Induced subgraph","score":0.3237000107765198}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8032000064849854},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7953000068664551},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.555400013923645},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5414999723434448},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5324000120162964},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4968999922275543},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.42899999022483826},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3977000117301941},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.3698999881744385},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.3237000107765198},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3203999996185303},{"id":"https://openalex.org/C128115575","wikidata":"https://www.wikidata.org/wiki/Q5597083","display_name":"Graph factorization","level":5,"score":0.29820001125335693},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.29170000553131104},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2863999903202057},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.25679999589920044},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.25380000472068787}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s0963548316000377","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548316000377","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A1FC8D7941DF0B67A3BA4DF9F90DE6B4/S0963548316000377a.pdf/div-class-title-saturated-graphs-of-prescribed-minimum-degree-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:arXiv.org:1407.6664","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1407.6664","pdf_url":"https://arxiv.org/pdf/1407.6664","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":null,"raw_type":"text"},{"id":"pmh:oai:qmro.qmul.ac.uk:123456789/19128","is_oa":false,"landing_page_url":"http://qmro.qmul.ac.uk/xmlui/handle/123456789/19128","pdf_url":null,"source":{"id":"https://openalex.org/S4306400530","display_name":"Queen Mary Research Online (Queen Mary University of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I166337079","host_organization_name":"Queen Mary University of London","host_organization_lineage":["https://openalex.org/I166337079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1017/s0963548316000377","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548316000377","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A1FC8D7941DF0B67A3BA4DF9F90DE6B4/S0963548316000377a.pdf/div-class-title-saturated-graphs-of-prescribed-minimum-degree-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":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1904326042.pdf","grobid_xml":"https://content.openalex.org/works/W1904326042.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1987231037","https://openalex.org/W1990490082","https://openalex.org/W1993471627","https://openalex.org/W2052840523","https://openalex.org/W2057226219","https://openalex.org/W2068795011","https://openalex.org/W2073286344","https://openalex.org/W2084913436","https://openalex.org/W2112243273","https://openalex.org/W4230975730"],"related_works":[],"abstract_inverted_index":{"A":[0],"graph":[1,58],"G":[2,24],"is":[3,89],"H":[4,12,29],"-saturated":[5,57],"if":[6,64],"it":[7,65],"contains":[8],"no":[9],"copy":[10,27],"of":[11,19,28,51,100],"as":[13,91],"a":[14,26,54,98],"subgraph":[15],"but":[16],"the":[17,38,48,87],"addition":[18],"any":[20],"new":[21,114],"edge":[22],"to":[23,46,94],"creates":[25],".":[30,72],"In":[31],"this":[32],"paper":[33],"we":[34],"are":[35],"interested":[36],"in":[37],"function":[39],"sat":[40,76,118],"t":[41,71,77,119],"(":[42,78,120],"n,p":[43,79,121],"),":[44],"defined":[45],"be":[47],"minimum":[49,67],"number":[50],"edges":[52],"that":[53,75,112],"K":[55],"p":[56,103],"on":[59],"n":[60,92],"vertices":[61],"can":[62],"have":[63],"has":[66],"degree":[68],"at":[69],"least":[70],"We":[73,106],"prove":[74],")":[80],"=":[81,104],"tn":[82],"\u2212":[83],"O":[84],"(1),":[85],"where":[86],"limit":[88],"taken":[90],"tends":[93],"infinity.":[95],"This":[96],"confirms":[97],"conjecture":[99],"Bollob\u00e1s":[101],"when":[102],"3.":[105],"also":[107],"present":[108],"constructions":[109],"for":[110,117],"graphs":[111],"give":[113],"upper":[115],"bounds":[116],").":[122]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2016-06-24T00:00:00"}
