{"id":"https://openalex.org/W7131827116","doi":"https://doi.org/10.48550/arxiv.2602.22856","title":"Results on three problems on isolation of graphs","display_name":"Results on three problems on isolation of graphs","publication_year":2026,"publication_date":"2026-02-26","ids":{"openalex":"https://openalex.org/W7131827116","doi":"https://doi.org/10.48550/arxiv.2602.22856"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.22856","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.22856","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2602.22856","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5127368385","display_name":"Peter Borg","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Borg, Peter","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5127441894","display_name":"Yair Caro","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Caro, Yair","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5127368385"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9908999800682068,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9908999800682068,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.002300000051036477,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.002099999925121665,"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/bounded-function","display_name":"Bounded function","score":0.6137999892234802},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5710999965667725},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4823000133037567},{"id":"https://openalex.org/keywords/dominating-set","display_name":"Dominating set","score":0.4050999879837036},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.34450000524520874},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3391000032424927}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6449000239372253},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6349999904632568},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6137999892234802},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5710999965667725},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4823000133037567},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.477400004863739},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.4050999879837036},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.34450000524520874},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3391000032424927},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.33070001006126404},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.2921000123023987},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2913999855518341},{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.27059999108314514},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.260699987411499},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.25999999046325684},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.22856","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.22856","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"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2602.22856","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.22856","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":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"graph":[1,20,68],"isolation":[2],"problem":[3,22,52],"was":[4],"introduced":[5],"by":[6,72],"Caro":[7],"and":[8,23,87,92],"Hansberg":[9],"in":[10,83,117],"2015.":[11],"It":[12],"is":[13,26,53,57,70,111],"a":[14,34,44,67,80],"vast":[15],"generalization":[16],"of":[17,36,66,77,85,90,99],"the":[18,49,62,73,88,95,120],"classical":[19],"domination":[21,115],"its":[24],"study":[25],"expanding":[27],"rapidly.":[28],"In":[29],"this":[30],"paper,":[31],"we":[32],"address":[33],"number":[35,64],"questions":[37],"that":[38,48],"arise":[39],"naturally.":[40],"Let":[41],"$F$":[42,56,91],"be":[43],"graph.":[45],"We":[46,59,105],"show":[47],"$F$-isolating":[50],"set":[51],"NP-complete":[54],"if":[55],"connected.":[58],"investigate":[60,107],"how":[61,108],"$F$-isolation":[63],"$\u03b9(G,F)$":[65,100],"$G$":[69],"affected":[71],"minimum":[74],"degree":[75],"$d$":[76,86,102],"$G$,":[78,93],"establishing":[79],"bounded":[81],"range,":[82],"terms":[84],"orders":[89],"for":[94],"largest":[96],"possible":[97],"value":[98],"with":[101],"sufficiently":[103],"large.":[104],"also":[106],"close":[109],"$\u03b9(G,tF)$":[110],"to":[112],"$\u03b9(G,F)$,":[113],"using":[114],"and,":[116],"suitable":[118],"cases,":[119],"Erdos-Posa":[121],"property.":[122]},"counts_by_year":[],"updated_date":"2026-02-28T06:18:59.386488","created_date":"2026-02-28T00:00:00"}
