{"id":"https://openalex.org/W2945570576","doi":"https://doi.org/10.37236/8767","title":"Covers, Orientations and Factors","display_name":"Covers, Orientations and Factors","publication_year":2020,"publication_date":"2020-08-07","ids":{"openalex":"https://openalex.org/W2945570576","doi":"https://doi.org/10.37236/8767","mag":"2945570576"},"language":"en","primary_location":{"id":"doi:10.37236/8767","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8767","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p25/pdf","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://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p25/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103170165","display_name":"P\u00e9ter Cs\u00edkv\u00e1ri","orcid":"https://orcid.org/0000-0001-6909-5253"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"P\u00e9ter Csikv\u00e1ri","raw_affiliation_strings":["Massachusetts Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017170857","display_name":"Andr\u00e1s Imolay","orcid":"https://orcid.org/0000-0002-1275-2950"},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Andr\u00e1s Imolay","raw_affiliation_strings":["ELTE, E\u00f6tv\u00f6s Lor\u00e1nd University"],"affiliations":[{"raw_affiliation_string":"ELTE, E\u00f6tv\u00f6s Lor\u00e1nd University","institution_ids":["https://openalex.org/I106118109"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103170165"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04911483,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11476","display_name":"Graph theory and applications","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9968000054359436,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9907000064849854,"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/eulerian-path","display_name":"Eulerian path","score":0.9132014513015747},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.8169671297073364},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7566479444503784},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6632543206214905},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5460169911384583},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5183821320533752},{"id":"https://openalex.org/keywords/simple-graph","display_name":"Simple graph","score":0.45277905464172363},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42575210332870483},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.42070090770721436},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10808470845222473},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.07230046391487122}],"concepts":[{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.9132014513015747},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.8169671297073364},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7566479444503784},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6632543206214905},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5460169911384583},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5183821320533752},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.45277905464172363},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42575210332870483},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.42070090770721436},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10808470845222473},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.07230046391487122},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/8767","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8767","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p25/pdf","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:1905.06678","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.06678","pdf_url":"https://arxiv.org/pdf/1905.06678","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":null},{"id":"mag:2945570576","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1905.06678v5","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:10.48550/arxiv.1905.06678","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1905.06678","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:10.37236/8767","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8767","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p25/pdf","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":[{"id":"https://metadata.un.org/sdg/10","score":0.49000000953674316,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1234428117","display_name":null,"funder_award_id":"EFOP-3.6.3-VEKOP-16-2017-00002","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"},{"id":"https://openalex.org/G1748000517","display_name":null,"funder_award_id":"NKFIH","funder_id":"https://openalex.org/F4320336675","funder_display_name":"National Research, Development and Innovation Office"},{"id":"https://openalex.org/G2689612763","display_name":null,"funder_award_id":"Marie","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2881119990","display_name":"Extremal Sparse Graphs and Graph Limits","funder_award_id":"747430","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3011850684","display_name":null,"funder_award_id":"EFOP-3.6.3-VEKOP-16-2017-00002","funder_id":"https://openalex.org/F4320338080","funder_display_name":"European Social Fund"},{"id":"https://openalex.org/G3279822479","display_name":null,"funder_award_id":"(EFOP-3.6.3-VEKOP-16-2017-00002)","funder_id":"https://openalex.org/F4320338080","funder_display_name":"European Social Fund"},{"id":"https://openalex.org/G3695840845","display_name":"Asymptotic invariants of discrete groups, sparse graphs and locally symmetric spaces","funder_award_id":"648017","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3998201246","display_name":null,"funder_award_id":"Social","funder_id":"https://openalex.org/F4320338080","funder_display_name":"European Social Fund"},{"id":"https://openalex.org/G4693063966","display_name":null,"funder_award_id":"EFOP-3","funder_id":"https://openalex.org/F4320338080","funder_display_name":"European Social Fund"},{"id":"https://openalex.org/G5374134968","display_name":null,"funder_award_id":"European Social Fund","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G570351115","display_name":null,"funder_award_id":"ERC Consolidator Grant 648017","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6551428496","display_name":null,"funder_award_id":"00002","funder_id":"https://openalex.org/F4320338080","funder_display_name":"European Social Fund"},{"id":"https://openalex.org/G7101391507","display_name":null,"funder_award_id":"EFOP-3.6.3-VEKOP-16","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/G8557630580","display_name":null,"funder_award_id":"co-financed","funder_id":"https://openalex.org/F4320338080","funder_display_name":"European Social Fund"},{"id":"https://openalex.org/G8712291568","display_name":null,"funder_award_id":"K109684","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"},{"id":"https://openalex.org/G8725523790","display_name":null,"funder_award_id":"EFOP-3.6.3-VEKOP-16","funder_id":"https://openalex.org/F4320338080","funder_display_name":"European Social Fund"},{"id":"https://openalex.org/G882585906","display_name":null,"funder_award_id":"NN114614","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"},{"id":"https://openalex.org/G972092959","display_name":null,"funder_award_id":"EFOP-3.6.3-VEKOP-16-2017-00002","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320326762","display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal","ror":null},{"id":"https://openalex.org/F4320336675","display_name":"National Research, Development and Innovation Office","ror":null},{"id":"https://openalex.org/F4320338080","display_name":"European Social Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2945570576.pdf","grobid_xml":"https://content.openalex.org/works/W2945570576.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1986646471","https://openalex.org/W2002234069","https://openalex.org/W2046106340","https://openalex.org/W2055585984","https://openalex.org/W2095087473","https://openalex.org/W2101478306","https://openalex.org/W2106299455","https://openalex.org/W2123934736","https://openalex.org/W2139671760","https://openalex.org/W2155237361","https://openalex.org/W2167490374","https://openalex.org/W2317309498","https://openalex.org/W2560801885","https://openalex.org/W2964087779","https://openalex.org/W2965754613","https://openalex.org/W3005342614","https://openalex.org/W3104688290","https://openalex.org/W3106495992"],"related_works":["https://openalex.org/W3082346739","https://openalex.org/W3044925268","https://openalex.org/W2514852333","https://openalex.org/W2110473668","https://openalex.org/W3081812744","https://openalex.org/W2955957317","https://openalex.org/W2087924811","https://openalex.org/W2798053658","https://openalex.org/W3181613994","https://openalex.org/W2586595016","https://openalex.org/W2620189872","https://openalex.org/W1545507519","https://openalex.org/W2462890351","https://openalex.org/W3014765870","https://openalex.org/W2570220149","https://openalex.org/W2899179943","https://openalex.org/W2884591311","https://openalex.org/W792346822","https://openalex.org/W2989730026","https://openalex.org/W3121197411"],"abstract_inverted_index":{"Given":[0],"a":[1,64,87,90],"graph":[2,91],"$G$":[3,56],"with":[4,50],"only":[5,54],"even":[6],"degrees,":[7],"let":[8,17],"$\\varepsilon(G)$":[9],"denote":[10,19],"the":[11,20,78],"number":[12,21,79],"of":[13,22,68,80,86,89],"Eulerian":[14,48,81],"orientations,":[15],"and":[16,38,53,71,75,83],"$h(G)$":[18],"half":[23,84],"graphs,":[24,49],"that":[25,30,41],"is,":[26],"subgraphs":[27],"$F$":[28],"such":[29],"$d_F(v)=d_G(v)/2$":[31],"for":[32,46,77],"each":[33],"vertex":[34],"$v$.":[35],"Recently,":[36],"Borb\u00e9nyi":[37],"Csikv\u00e1ri":[39],"proved":[40],"$\\varepsilon(G)\\geq":[42],"h(G)$":[43],"holds":[44],"true":[45],"all":[47],"equality":[51],"if":[52,55],"is":[57],"bipartite.":[58],"In":[59],"this":[60,69],"paper":[61],"we":[62,72],"give":[63,73],"simple":[65],"new":[66],"proof":[67],"fact,":[70],"identities":[74],"inequalities":[76],"orientations":[82],"graphs":[85],"$2$-cover":[88],"$G$.":[92]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
