{"id":"https://openalex.org/W4416513685","doi":"https://doi.org/10.48550/arxiv.2506.23363","title":"Parameterized Critical Node Cut Revisited","display_name":"Parameterized Critical Node Cut Revisited","publication_year":2025,"publication_date":"2025-06-29","ids":{"openalex":"https://openalex.org/W4416513685","doi":"https://doi.org/10.48550/arxiv.2506.23363"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2506.23363","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.23363","pdf_url":"https://arxiv.org/pdf/2506.23363","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2506.23363","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073361240","display_name":"Du\u0161an Knop","orcid":"https://orcid.org/0000-0003-2588-5709"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Knop, Du\u0161an","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088003340","display_name":"Nikolaos Melissinos","orcid":"https://orcid.org/0000-0002-0864-9803"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Melissinos, Nikolaos","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5037706878","display_name":"Manolis Vasilakis","orcid":"https://orcid.org/0000-0001-6505-2977"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vasilakis, Manolis","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5073361240"],"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.4025999903678894,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.4025999903678894,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.28999999165534973,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.12200000137090683,"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/vertex-cover","display_name":"Vertex cover","score":0.7651000022888184},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.7312999963760376},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.6291999816894531},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.6032999753952026},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5297999978065491},{"id":"https://openalex.org/keywords/edge-cover","display_name":"Edge cover","score":0.48980000615119934},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.48750001192092896},{"id":"https://openalex.org/keywords/feedback-vertex-set","display_name":"Feedback vertex set","score":0.4713999927043915},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.42010000348091125},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.38600000739097595}],"concepts":[{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.7651000022888184},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.7312999963760376},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.6291999816894531},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.6032999753952026},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6021999716758728},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5878000259399414},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5297999978065491},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5062999725341797},{"id":"https://openalex.org/C17762858","wikidata":"https://www.wikidata.org/wiki/Q594001","display_name":"Edge cover","level":3,"score":0.48980000615119934},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.48750001192092896},{"id":"https://openalex.org/C28723256","wikidata":"https://www.wikidata.org/wiki/Q1400918","display_name":"Feedback vertex set","level":4,"score":0.4713999927043915},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.42010000348091125},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.38600000739097595},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.3580000102519989},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.3400000035762787},{"id":"https://openalex.org/C187407849","wikidata":"https://www.wikidata.org/wiki/Q6889712","display_name":"Modular decomposition","level":5,"score":0.3346000015735626},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.3312999904155731},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.32679998874664307},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.32350000739097595},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.32339999079704285},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.32269999384880066},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28839999437332153},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.28459998965263367},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.2838999927043915},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C18359143","wikidata":"https://www.wikidata.org/wiki/Q7888149","display_name":"Maximal independent set","level":5,"score":0.28040000796318054},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.27869999408721924},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2768000066280365},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.275299996137619},{"id":"https://openalex.org/C186942658","wikidata":"https://www.wikidata.org/wiki/Q5134410","display_name":"Clique-sum","level":5,"score":0.27309998869895935},{"id":"https://openalex.org/C160446489","wikidata":"https://www.wikidata.org/wiki/Q7226642","display_name":"Polynomial kernel","level":4,"score":0.2581999897956848},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.2542000114917755},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2540000081062317},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.2538999915122986}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2506.23363","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.23363","pdf_url":"https://arxiv.org/pdf/2506.23363","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:doi:10.48550/arxiv.2506.23363","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2506.23363","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2506.23363","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":"pmh:oai:arXiv.org:2506.23363","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.23363","pdf_url":"https://arxiv.org/pdf/2506.23363","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"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":{"We":[0,68],"study":[1],"how":[2],"to":[3],"sparsify":[4],"connectivity":[5],"in":[6,60,132,198],"graphs":[7,170],"under":[8],"a":[9,14,166,176,195],"tight":[10,131],"deletion":[11],"budget.":[12],"Given":[13],"graph":[15,113],"$G$":[16],"and":[17,57,64,106,129,157,164],"integers":[18],"$k,x":[19],"\\ge":[20],"0$,":[21,193],"Critical":[22,77],"Node":[23,78],"Cut":[24],"(CNC)":[25],"asks":[26],"whether":[27],"we":[28,81,143,149,182,214],"can":[29],"delete":[30],"at":[31,47],"most":[32,48],"$k$":[33],"vertices":[34,45],"so":[35],"that":[36,133,216],"the":[37,71,85,97,103,108,111,119,127,160,207,210,237],"number":[38],"of":[39,43,110,171,209],"remaining":[40],"unordered":[41],"pairs":[42],"connected":[44],"is":[46,96,130],"$x$.":[49],"CNC":[50,217],"generalizes":[51],"Vertex":[52],"Cover":[53],"(the":[54],"case":[55],"$x=0$)":[56],"models":[58],"tasks":[59],"network":[61,66],"design,":[62],"epidemiology,":[63],"social":[65],"analysis.":[67],"comprehensively":[69],"map":[70],"structural":[72,152],"parameterized":[73,223],"complexity":[74,239],"landscape":[75,240],"for":[76,84,122,169,189,241],"Cut.":[79],"First,":[80],"prove":[82],"W[1]-hardness":[83,121],"combined":[86],"parameter":[87],"$k":[88],"+":[89,91],"\\mathrm{fes}":[90],"\u0394+":[92],"\\mathrm{pw}$,":[93],"where":[94,124,204],"$\\mathrm{fes}$":[95],"feedback":[98],"edge":[99],"set":[100],"number,":[101,154,227],"$\u0394$":[102],"maximum":[104,137],"degree,":[105],"$\\mathrm{pw}$":[107],"pathwidth":[109],"input":[112,211],"respectively.":[114],"This":[115],"significantly":[116],"improves":[117],"over":[118],"known":[120,238],"$k+\\mathrm{tw}$,":[123],"$\\mathrm{tw}$":[125,205],"denotes":[126,206],"treewidth,":[128],"tree-depth":[134],"together":[135],"with":[136],"degree":[138],"trivially":[139],"yields":[140],"FPT.":[141],"Second,":[142],"give":[144],"new":[145],"positive":[146],"results.":[147],"Specifically,":[148],"identify":[150],"three":[151],"parameters--max-leaf":[153],"vertex":[155,225],"integrity,":[156],"modular-width--that":[158],"render":[159],"problem":[161],"fixed-parameter":[162],"tractable,":[163],"develop":[165,183],"polynomial-time":[167],"algorithm":[168],"constant":[172],"clique-width.":[173],"Third,":[174],"leveraging":[175],"technique":[177],"introduced":[178],"by":[179,224],"Lampis~[ICALP":[180],"'14],":[181],"an":[184],"FPT":[185],"approximation":[186],"scheme":[187],"that,":[188],"any":[190],"$\\varepsilon":[191],">":[192],"computes":[194],"$(1+\\varepsilon)$-approximate":[196],"solution":[197],"time":[199],"$(\\mathrm{tw}":[200],"/":[201],"\\varepsilon)^{\\mathcal{O}(\\mathrm{tw})}":[202],"n^{\\mathcal{O}(1)}$,":[203],"treewidth":[208],"graph.":[212],"Finally,":[213],"show":[215],"admits":[218],"no":[219],"polynomial":[220],"kernel":[221],"when":[222],"cover":[226],"unless":[228],"standard":[229],"assumptions":[230],"fail.":[231],"Together,":[232],"these":[233],"results":[234],"substantially":[235],"sharpen":[236],"CNC.":[242]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}