{"id":"https://openalex.org/W2955236601","doi":"https://doi.org/10.4230/lipics.esa.2019.72","title":"Packing Directed Circuits Quarter-Integrally","display_name":"Packing Directed Circuits Quarter-Integrally","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2955236601","doi":"https://doi.org/10.4230/lipics.esa.2019.72","mag":"2955236601"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:11193","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.72","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"InProceedings"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.72","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027217082","display_name":"Tom\u00e1\u0161 Masa\u0159\u00edk","orcid":"https://orcid.org/0000-0001-8524-4036"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]},{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["CZ","PL"],"is_corresponding":true,"raw_author_name":"Masa\u0159\u00edk, Tom\u00e1\u0161","raw_affiliation_strings":["Department of Applied Mathematics, Charles University, Prague, Czech Republic & Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Charles University, Prague, Czech Republic & Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613","https://openalex.org/I21250087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048273965","display_name":"Irene Muzi","orcid":"https://orcid.org/0000-0003-2410-6523"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Muzi, Irene","raw_affiliation_strings":["Technische Universit\u00e4t Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059330513","display_name":"Marcin Pilipczuk","orcid":"https://orcid.org/0000-0001-5680-7397"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Pilipczuk, Marcin","raw_affiliation_strings":["Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047941027","display_name":"Pawe\u0142 Rz\u0105\u017cewski","orcid":"https://orcid.org/0000-0001-7696-3848"},"institutions":[{"id":"https://openalex.org/I108403487","display_name":"Warsaw University of Technology","ror":"https://ror.org/00y0xnp53","country_code":"PL","type":"education","lineage":["https://openalex.org/I108403487"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Rz\u0105\u017cewski, Pawe\u0142","raw_affiliation_strings":["Faculty of Mathematics and Information Science, Warsaw University of Technology, Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Information Science, Warsaw University of Technology, Warsaw, Poland","institution_ids":["https://openalex.org/I108403487"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033440939","display_name":"Manuel Sorge","orcid":"https://orcid.org/0000-0001-7394-3147"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Sorge, Manuel","raw_affiliation_strings":["Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5027217082"],"corresponding_institution_ids":["https://openalex.org/I21250087","https://openalex.org/I4654613"],"apc_list":null,"apc_paid":null,"fwci":0.3991,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.64055642,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"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":0.9987000226974487,"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":0.9987000226974487,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9951000213623047,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9908000230789185,"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/combinatorics","display_name":"Combinatorics","score":0.8864946365356445},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7434691190719604},{"id":"https://openalex.org/keywords/feedback-vertex-set","display_name":"Feedback vertex set","score":0.6781138181686401},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.6087546348571777},{"id":"https://openalex.org/keywords/feedback-arc-set","display_name":"Feedback arc set","score":0.5872735977172852},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5689433217048645},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5068281292915344},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.500718355178833},{"id":"https://openalex.org/keywords/neighbourhood","display_name":"Neighbourhood (mathematics)","score":0.4779938757419586},{"id":"https://openalex.org/keywords/undirected-graph","display_name":"Undirected graph","score":0.45037731528282166},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.4148518443107605},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.37192803621292114},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.3005174398422241},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.17302358150482178},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.06609049439430237}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8864946365356445},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7434691190719604},{"id":"https://openalex.org/C28723256","wikidata":"https://www.wikidata.org/wiki/Q1400918","display_name":"Feedback vertex set","level":4,"score":0.6781138181686401},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.6087546348571777},{"id":"https://openalex.org/C157951044","wikidata":"https://www.wikidata.org/wiki/Q1400910","display_name":"Feedback arc set","level":5,"score":0.5872735977172852},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5689433217048645},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5068281292915344},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.500718355178833},{"id":"https://openalex.org/C161677786","wikidata":"https://www.wikidata.org/wiki/Q2478475","display_name":"Neighbourhood (mathematics)","level":2,"score":0.4779938757419586},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.45037731528282166},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.4148518443107605},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.37192803621292114},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.3005174398422241},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.17302358150482178},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.06609049439430237},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:11193","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.72","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"InProceedings"},{"id":"mag:2955236601","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1907.02494v2","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":"doi:10.4230/lipics.esa.2019.72","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.esa.2019.72","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:11193","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.72","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"InProceedings"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3634255087","display_name":"Structure Theory for Directed Graphs","funder_award_id":"648527","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4956428346","display_name":null,"funder_award_id":"Horizon 2020 research and innovatio","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5036817778","display_name":null,"funder_award_id":"European Union's Horizon 2020 research and innov","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5244030528","display_name":null,"funder_award_id":"714704","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8051717526","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8318064016","display_name":null,"funder_award_id":"Horizon","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8633428685","display_name":null,"funder_award_id":"European Union's Horizon 2020 research and innovat","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320309755","display_name":"Univerzita Karlova v Praze","ror":"https://ror.org/024d6js02"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320324094","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2165731524","https://openalex.org/W1588670023","https://openalex.org/W1793690078","https://openalex.org/W3006483437","https://openalex.org/W2747174799","https://openalex.org/W2067380255","https://openalex.org/W2746485617","https://openalex.org/W2172105872","https://openalex.org/W2911978162","https://openalex.org/W2949613875","https://openalex.org/W2952856253","https://openalex.org/W2074084387","https://openalex.org/W3048492929","https://openalex.org/W2883156479","https://openalex.org/W2765360845","https://openalex.org/W2811405330","https://openalex.org/W3012421265","https://openalex.org/W2964281044","https://openalex.org/W2921118110","https://openalex.org/W301992243"],"abstract_inverted_index":{"The":[0],"celebrated":[1],"Erd\u0151s-P\u00f3sa":[2],"theorem":[3],"states":[4],"that":[5,9,90,120,135,218],"every":[6,136,180,219],"undirected":[7],"graph":[8,105,125,191],"does":[10],"not":[11,86],"admit":[12],"a":[13,20,47,97,103,113,123,151,166,185,189,205,208],"family":[14,130,206],"of":[15,26,34,70,73,81,96,131,138,145,157,173,175,182,207,211,221],"k":[16,132],"vertex-disjoint":[17,82],"cycles":[18,30,133],"contains":[19],"feedback":[21,75,99,152],"vertex":[22,76,100,137,153,220],"set":[23,25,77,101,154],"(a":[24],"vertices":[27],"hitting":[28],"all":[29],"in":[31,56,65,102,122,141,155,203,224],"the":[32,68,71,74,79,94,146,161],"graph)":[33],"size":[35,72,80,95,158],"O(k":[36],"log":[37],"k).":[38],"After":[39],"being":[40],"known":[41],"for":[42,50,179],"long":[43],"as":[44],"Younger\u2019s":[45],"conjecture,":[46],"similar":[48],"statement":[49],"directed":[51,104,124,177,190,194,212],"graphs":[52],"has":[53,193],"been":[54],"proven":[55],"1996":[57],"by":[58],"Reed,":[59],"Robertson,":[60],"Seymour,":[61],"and":[62,186],"Thomas.":[63],"However,":[64],"their":[66],"proof,":[67],"dependency":[69],"on":[78],"cycle":[83,108],"packing":[84,109,172],"is":[85,128,140,223],"elementary.":[87],"We":[88],"show":[89,119],"if":[91,121,188],"we":[92,111,118,164],"compare":[93],"minimum":[98],"with":[106],"quarter-integral":[107,171],"number,":[110],"obtain":[112],"polynomial":[114],"bound.":[115],"More":[116],"precisely,":[117],"G":[126,139,156,192,204,222],"there":[127,149,163],"no":[129],"such":[134,217],"at":[142,214,225],"most":[143,226],"four":[144,227],"cycles,":[147],"then":[148,199],"exists":[150],"O(k^4).":[159],"On":[160],"way":[162],"prove":[165],"more":[167],"general":[168],"result":[169],"about":[170],"subgraphs":[174],"high":[176],"treewidth:":[178],"pair":[181],"positive":[183],"integers":[184],"b,":[187,216],"treewidth":[195,213],"Omega(a^6":[196],"b^8":[197],"log^2(ab)),":[198],"one":[200],"can":[201],"find":[202],"subgraphs,":[209],"each":[210],"least":[215],"subgraphs.":[228]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-11T14:59:36.786465","created_date":"2025-10-10T00:00:00"}
