{"id":"https://openalex.org/W2954749300","doi":"https://doi.org/10.37236/9486","title":"The $k$-Cut Model in Deterministic and Random Trees","display_name":"The $k$-Cut Model in Deterministic and Random Trees","publication_year":2021,"publication_date":"2021-01-29","ids":{"openalex":"https://openalex.org/W2954749300","doi":"https://doi.org/10.37236/9486","mag":"2954749300"},"language":"en","primary_location":{"id":"doi:10.37236/9486","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9486","pdf_url":null,"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://doi.org/10.37236/9486","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066672201","display_name":"Gabriel Berzunza","orcid":null},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Gabriel Berzunza","raw_affiliation_strings":["Uppsala University"],"affiliations":[{"raw_affiliation_string":"Uppsala University","institution_ids":["https://openalex.org/I123387679"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008760479","display_name":"Xing Shi Cai","orcid":"https://orcid.org/0000-0002-3768-8078"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Xing Shi Cai","raw_affiliation_strings":["Uppsala University"],"affiliations":[{"raw_affiliation_string":"Uppsala University","institution_ids":["https://openalex.org/I123387679"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018224596","display_name":"Cecilia Holmgren","orcid":"https://orcid.org/0000-0003-0717-4671"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Cecilia Holmgren","raw_affiliation_strings":["Uppsala University"],"affiliations":[{"raw_affiliation_string":"Uppsala University","institution_ids":["https://openalex.org/I123387679"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5066672201"],"corresponding_institution_ids":["https://openalex.org/I123387679"],"apc_list":null,"apc_paid":null,"fwci":0.455,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.49677776,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"28","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9998000264167786,"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/T11106","display_name":"Data Management and Algorithms","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10591","display_name":"Theoretical and Computational Physics","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8195037841796875},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5899959802627563},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5222816467285156},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5128834247589111},{"id":"https://openalex.org/keywords/random-tree","display_name":"Random tree","score":0.4906715154647827},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.479714572429657},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.47265684604644775},{"id":"https://openalex.org/keywords/convergence-of-random-variables","display_name":"Convergence of random variables","score":0.46919605135917664},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.4613203704357147},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.45843252539634705},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4307989776134491},{"id":"https://openalex.org/keywords/random-variate","display_name":"Random variate","score":0.42179811000823975},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4127955138683319},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.41111433506011963},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.2732017934322357},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.270346462726593},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14497724175453186},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11116060614585876},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0849277675151825}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8195037841796875},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5899959802627563},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5222816467285156},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5128834247589111},{"id":"https://openalex.org/C2776839635","wikidata":"https://www.wikidata.org/wiki/Q14942679","display_name":"Random tree","level":4,"score":0.4906715154647827},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.479714572429657},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.47265684604644775},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.46919605135917664},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.4613203704357147},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.45843252539634705},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4307989776134491},{"id":"https://openalex.org/C141547133","wikidata":"https://www.wikidata.org/wiki/Q7291996","display_name":"Random variate","level":3,"score":0.42179811000823975},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4127955138683319},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.41111433506011963},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2732017934322357},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.270346462726593},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14497724175453186},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11116060614585876},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0849277675151825},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.0},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C81074085","wikidata":"https://www.wikidata.org/wiki/Q366872","display_name":"Motion planning","level":3,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/9486","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9486","pdf_url":null,"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:arXiv.org:1907.02770","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.02770","pdf_url":"https://arxiv.org/pdf/1907.02770","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":"mag:2954749300","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1907.02770","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:DiVA.org:uu-440416","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-440416","pdf_url":null,"source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article in journal"},{"id":"doi:10.48550/arxiv.1907.02770","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1907.02770","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:10.37236/9486","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9486","pdf_url":null,"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":[{"display_name":"Peace, Justice and strong institutions","score":0.49000000953674316,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W32539110","https://openalex.org/W183507914","https://openalex.org/W1499059270","https://openalex.org/W1545370368","https://openalex.org/W1584623820","https://openalex.org/W1963890374","https://openalex.org/W1971974071","https://openalex.org/W1978667133","https://openalex.org/W2008620264","https://openalex.org/W2011952756","https://openalex.org/W2017170340","https://openalex.org/W2020389755","https://openalex.org/W2022069198","https://openalex.org/W2022718961","https://openalex.org/W2029013046","https://openalex.org/W2033659213","https://openalex.org/W2043092396","https://openalex.org/W2049571660","https://openalex.org/W2060679341","https://openalex.org/W2063183361","https://openalex.org/W2074639950","https://openalex.org/W2081564088","https://openalex.org/W2090228192","https://openalex.org/W2095181329","https://openalex.org/W2107808918","https://openalex.org/W2152197249","https://openalex.org/W2157071288","https://openalex.org/W2752853835","https://openalex.org/W2914483255","https://openalex.org/W2916538292","https://openalex.org/W2962801705","https://openalex.org/W3091874817","https://openalex.org/W3097979267","https://openalex.org/W3100171672","https://openalex.org/W3104565967"],"related_works":["https://openalex.org/W3043853901","https://openalex.org/W2753856963","https://openalex.org/W1993876690","https://openalex.org/W2028873372","https://openalex.org/W1530167487","https://openalex.org/W1549761076","https://openalex.org/W2142568813","https://openalex.org/W2952084565","https://openalex.org/W1996508950","https://openalex.org/W3083134037","https://openalex.org/W2073698762","https://openalex.org/W3013788123","https://openalex.org/W2131732906","https://openalex.org/W2066540443","https://openalex.org/W3204705411","https://openalex.org/W3010411929","https://openalex.org/W3106534834","https://openalex.org/W2962750324","https://openalex.org/W3015214280","https://openalex.org/W2963859154"],"abstract_inverted_index":{"The":[0],"\\(k\\)-cut":[1,34,77],"number":[2,35,78],"of":[3,15,32,36,55,59,66,79,85],"rooted":[4],"graphs":[5],"was":[6],"introduced":[7],"by":[8,20],"Cai":[9],"et":[10],"al.":[11],"as":[12,97],"a":[13,92],"generalization":[14],"the":[16,33,50,56,60,64,69,76],"classical":[17],"cutting":[18],"model":[19],"Meir":[21],"and":[22,104],"Moon.":[23],"In":[24],"this":[25],"paper,":[26],"we":[27,72],"show":[28,74],"that":[29,75],"all":[30],"moments":[31],"conditioned":[37],"Galton-Watson":[38],"trees":[39,84],"converge":[40],"after":[41,94],"proper":[42],"rescaling,":[43,95],"which":[44],"implies":[45],"convergence":[46],"in":[47,89],"distribution":[48,58],"to":[49,91],"same":[51,70],"limit":[52],"law":[53],"regardless":[54],"offspring":[57],"trees.":[61,107],"This":[62],"extends":[63],"result":[65],"Janson.":[67],"Using":[68],"method,":[71],"also":[73],"various":[80],"random":[81,98,101,106],"or":[82],"deterministic":[83],"logarithmic":[86],"height":[87],"converges":[88],"probability":[90],"constant":[93],"such":[96],"split-trees,":[99],"uniform":[100],"recursive":[102],"trees,":[103],"scale-free":[105]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
