{"id":"https://openalex.org/W4399095150","doi":"https://doi.org/10.1007/s00493-024-00108-0","title":"Arc Connectivity and Submodular Flows in Digraphs","display_name":"Arc Connectivity and Submodular Flows in Digraphs","publication_year":2024,"publication_date":"2024-05-28","ids":{"openalex":"https://openalex.org/W4399095150","doi":"https://doi.org/10.1007/s00493-024-00108-0"},"language":"lv","primary_location":{"id":"doi:10.1007/s00493-024-00108-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-024-00108-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-024-00108-0.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00493-024-00108-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075655329","display_name":"Ahmad Abdi","orcid":"https://orcid.org/0000-0002-3008-4167"},"institutions":[{"id":"https://openalex.org/I909854389","display_name":"London School of Economics and Political Science","ror":"https://ror.org/0090zs177","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I909854389"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Ahmad Abdi","raw_affiliation_strings":["London School of Economics and Political Science, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"London School of Economics and Political Science, London, UK","institution_ids":["https://openalex.org/I909854389"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014470090","display_name":"G\u00e9rard Cornu\u00e9jols","orcid":"https://orcid.org/0000-0002-3976-1021"},"institutions":[{"id":"https://openalex.org/I909854389","display_name":"London School of Economics and Political Science","ror":"https://ror.org/0090zs177","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I909854389"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"G\u00e9rard Cornu\u00e9jols","raw_affiliation_strings":["London School of Economics and Political Science, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"London School of Economics and Political Science, London, UK","institution_ids":["https://openalex.org/I909854389"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033378505","display_name":"Giacomo Zambelli","orcid":"https://orcid.org/0000-0003-3147-3938"},"institutions":[{"id":"https://openalex.org/I909854389","display_name":"London School of Economics and Political Science","ror":"https://ror.org/0090zs177","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I909854389"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Giacomo Zambelli","raw_affiliation_strings":["London School of Economics and Political Science, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"London School of Economics and Political Science, London, UK","institution_ids":["https://openalex.org/I909854389"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5075655329"],"corresponding_institution_ids":["https://openalex.org/I909854389"],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":{"value":3190,"currency":"USD","value_usd":3190},"fwci":0.4771,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.64561698,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"44","issue":"5","first_page":"1069","last_page":"1090"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"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":0.9975000023841858,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/mathematics","display_name":"Mathematics","score":0.8433268070220947},{"id":"https://openalex.org/keywords/arc","display_name":"Arc (geometry)","score":0.8341079950332642},{"id":"https://openalex.org/keywords/submodular-set-function","display_name":"Submodular set function","score":0.8140277862548828},{"id":"https://openalex.org/keywords/digraph","display_name":"Digraph","score":0.6889533996582031},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6737931370735168},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3767469525337219},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13023871183395386}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8433268070220947},{"id":"https://openalex.org/C83415579","wikidata":"https://www.wikidata.org/wiki/Q161973","display_name":"Arc (geometry)","level":2,"score":0.8341079950332642},{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.8140277862548828},{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.6889533996582031},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6737931370735168},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3767469525337219},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13023871183395386}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00493-024-00108-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-024-00108-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-024-00108-0.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},{"id":"pmh:oai:researchonline.lse.ac.uk:122866","is_oa":true,"landing_page_url":"https://orcid.org/0000-0002-3008-4167>,","pdf_url":"https://researchonline.lse.ac.uk/id/eprint/122866/3/Abdi_arc-connectivity--published.pdf","source":{"id":"https://openalex.org/S4306401593","display_name":"London School of Economics and Political Science Research Online (London School of Economics and Political Science)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I909854389","host_organization_name":"London School of Economics and Political Science","host_organization_lineage":["https://openalex.org/I909854389"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s00493-024-00108-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-024-00108-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-024-00108-0.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1463291576","display_name":null,"funder_award_id":"EP/X030989/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1528488193","display_name":null,"funder_award_id":"N00014-22-1-2528","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G4720003262","display_name":null,"funder_award_id":"N00014-22","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8695986878","display_name":"New perspectives towards Woodall's Conjecture and the Generalised Berge-Fulkerson Conjecture","funder_award_id":"EP/X030989/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320314731","display_name":"UK Research and Innovation","ror":"https://ror.org/001aqnf71"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4399095150.pdf","grobid_xml":"https://content.openalex.org/works/W4399095150.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W122420714","https://openalex.org/W1508474907","https://openalex.org/W1604158939","https://openalex.org/W1975433230","https://openalex.org/W2000317174","https://openalex.org/W2010006094","https://openalex.org/W2032711721","https://openalex.org/W2042275390","https://openalex.org/W2042706982","https://openalex.org/W2058858486","https://openalex.org/W2115687272","https://openalex.org/W2124531440","https://openalex.org/W2887196600","https://openalex.org/W2913508203","https://openalex.org/W2988480584","https://openalex.org/W3026619919","https://openalex.org/W4294733420","https://openalex.org/W4387779581"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1997613377","https://openalex.org/W1930841953","https://openalex.org/W2393730076","https://openalex.org/W3195942359","https://openalex.org/W2885112897","https://openalex.org/W2782194400","https://openalex.org/W2012554677","https://openalex.org/W2624428482","https://openalex.org/W2075582476"],"abstract_inverted_index":{"Abstract":[0],"Let":[1,159],"$$D=(V,A)$$":[2],"D":[3,32],"=":[4],"(":[5,97,101,110,135,143,194,200],"V":[6,124,170],",":[7,21,88,125,129,157,171],"A":[8,95,108,133,141,152,202],")":[9,99,106,112,137,145,196],"be":[10,163,183],"a":[11,22,55,62,69,73,164,184],"digraph.":[12],"For":[13],"an":[14,28],"integer":[15,81],"$$k\\ge":[16],"1$$":[17,84],"k":[18,23,45,63,103,198],"\u2265":[19,86,113,197],"1":[20,87,105],"-":[24,104,109,142],"arc-connected":[25],"flip":[26,65],"is":[27,67],"arc":[29],"subset":[30],"of":[31,51,61,149],"such":[33,188],"that":[34,66,189],"after":[35],"reversing":[36],"the":[37,41,59,147],"arcs":[38,150],"in":[39,151],"it":[40],"digraph":[42],"becomes":[43],"(strongly)":[44],"-arc-connected.":[46],"The":[47],"first":[48],"main":[49],"result":[50],"this":[52],"paper":[53],"introduces":[54],"sufficient":[56],"condition":[57],"for":[58,72,115],"existence":[60],"-arc-connected":[64],"also":[68],"submodular":[70,75,186],"flow":[71],"crossing":[74,165,185],"function.":[76],"More":[77],"specifically,":[78],"given":[79],"some":[80],"$$\\tau":[82],"\\ge":[83],"\u03c4":[85,102,114,199],"suppose":[89],"$$d_A^+(U)+(\\frac{\\tau":[90],"}{k}-1)d_A^-(U)\\ge":[91],"\\tau":[92],"$$":[93,121],"d":[94,107,132,140,201],"+":[96,100,134],"U":[98,111,122,126,136,144,156,195],"all":[116],"$$U\\subsetneq":[117],"V,":[118],"U\\ne":[119],"\\emptyset":[120],"\u228a":[123],"\u2260":[127],"\u2205":[128],"where":[130],"$$d_A^+(U)$$":[131],"and":[138,154,172],"$$d_A^-(U)$$":[139],"denote":[146],"number":[148],"leaving":[153],"entering":[155],"respectively.":[158],"$${\\mathcal":[160],"{C}}$$":[161],"C":[162,180],"family":[166],"over":[167],"ground":[168],"set":[169],"let":[173],"$$f:{\\mathcal":[174],"{C}}\\rightarrow":[175],"{\\mathbb":[176],"{Z}}$$":[177],"f":[178,193],":":[179],"\u2192":[181],"Z":[182],"function":[187],"$$f(U)\\ge":[190],"\\frac{k}{\\tau":[191],"}(d_A^+(U)-d_A^-(U))$$":[192]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-09-03T10:48:47.769340","created_date":"2025-10-10T00:00:00"}
