{"id":"https://openalex.org/W3112691972","doi":"https://doi.org/10.37236/9579","title":"$P_{n}$-Induced-Saturated Graphs Exist for all $n \\geqslant 6$","display_name":"$P_{n}$-Induced-Saturated Graphs Exist for all $n \\geqslant 6$","publication_year":2020,"publication_date":"2020-12-11","ids":{"openalex":"https://openalex.org/W3112691972","doi":"https://doi.org/10.37236/9579","mag":"3112691972"},"language":"en","primary_location":{"id":"doi:10.37236/9579","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9579","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p43/pdf","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":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p43/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101813272","display_name":"Vojt\u011bch Dvo\u0159\u00e1k","orcid":"https://orcid.org/0000-0001-6483-7342"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Vojt\u011bch Dvo\u0159\u00e1k","raw_affiliation_strings":["University of Cambridge"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Cambridge","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101813272"],"corresponding_institution_ids":["https://openalex.org/I241749"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.3226601,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"4","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":0.9922000169754028,"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":0.9922000169754028,"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":0.9850000143051147,"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/T11157","display_name":"Chronic Lymphocytic Leukemia Research","score":0.9797999858856201,"subfield":{"id":"https://openalex.org/subfields/2716","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8427854776382446},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7735924124717712},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5207826495170593},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4425477981567383}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8427854776382446},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7735924124717712},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5207826495170593},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4425477981567383}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/9579","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9579","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p43/pdf","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"}],"best_oa_location":{"id":"doi:10.37236/9579","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9579","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p43/pdf","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3112691972.pdf","grobid_xml":"https://content.openalex.org/works/W3112691972.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W2025125798","https://openalex.org/W2161173317","https://openalex.org/W2792965417","https://openalex.org/W2963574837","https://openalex.org/W3080511195"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596","https://openalex.org/W4238204885"],"abstract_inverted_index":{"Let":[0],"$P_{n}$":[1],"be":[2],"a":[3,12,43,87,111],"path":[4],"graph":[5,13,88],"on":[6],"$n$":[7],"vertices.":[8],"We":[9,108],"say":[10],"that":[11,50,114],"$G$":[14,18,30,36],"is":[15,52],"$P_{n}$-induced-saturated":[16,63,81,115],"if":[17],"contains":[19],"no":[20,53],"induced":[21],"copy":[22],"of":[23,29,39],"$P_{n}$,":[24],"but":[25],"deleting":[26],"any":[27,37],"edge":[28,38],"as":[31,33],"well":[32],"adding":[34],"to":[35],"$G^{c}$":[40],"creates":[41],"such":[42,86,99],"copy.":[44],"Martin":[45],"and":[46,68,91,94],"Smith":[47],"(2012)":[48],"showed":[49],"there":[51,60,79],"$P_{4}$-induced-saturated":[54],"graph.":[55],"On":[56],"the":[57,125],"other":[58],"hand,":[59],"trivially":[61],"exist":[62,80,117],"graphs":[64,100,116],"for":[65,72,89,101,104,118],"$n=2,3$.":[66],"Axenovich":[67],"Csik\u00f3s":[69],"(2019)":[70,84,96],"ask":[71],"which":[73],"integers":[74],"$n":[75,120],"\\geqslant":[76,106,121],"5$":[77],"do":[78],"graphs.":[82],"R\u00e4ty":[83],"constructed":[85,98],"$n=6$,":[90],"Cho,":[92],"Choi":[93],"Park":[95],"later":[97],"all":[102,119],"$n=3k$":[103],"$k":[105],"2$.":[107],"show":[109],"by":[110],"different":[112],"construction":[113],"6$,":[122],"leaving":[123],"only":[124],"case":[126],"$n=5$":[127],"open.":[128]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}