{"id":"https://openalex.org/W4318769212","doi":"https://doi.org/10.1137/22m1472425","title":"5-Cycle Double Covers, 4-Flows, and Catlin Reduction","display_name":"5-Cycle Double Covers, 4-Flows, and Catlin Reduction","publication_year":2023,"publication_date":"2023-02-02","ids":{"openalex":"https://openalex.org/W4318769212","doi":"https://doi.org/10.1137/22m1472425"},"language":"en","primary_location":{"id":"doi:10.1137/22m1472425","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/22m1472425","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050820498","display_name":"Siyan Liu","orcid":"https://orcid.org/0000-0003-2017-3251"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Siyan Liu","raw_affiliation_strings":["School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, People\u2019s Republic of China","School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, People\u2019s Republic of China","institution_ids":["https://openalex.org/I21193070"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, People's Republic of China","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049116158","display_name":"Rong\u2010Xia Hao","orcid":"https://orcid.org/0000-0001-8714-8750"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rong-Xia Hao","raw_affiliation_strings":["Corresponding author. School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Corresponding author. School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, People\u2019s Republic of China","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066405314","display_name":"Rong Luo","orcid":"https://orcid.org/0000-0002-5237-1001"},"institutions":[{"id":"https://openalex.org/I12097938","display_name":"West Virginia University","ror":"https://ror.org/011vxgd24","country_code":"US","type":"education","lineage":["https://openalex.org/I12097938"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rong Luo","raw_affiliation_strings":["Department of Mathematics, West Virginia University, Morgantown, WV 26506 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, West Virginia University, Morgantown, WV 26506 USA","institution_ids":["https://openalex.org/I12097938"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064703404","display_name":"Cun\u2010Quan Zhang","orcid":"https://orcid.org/0000-0001-5583-4481"},"institutions":[{"id":"https://openalex.org/I12097938","display_name":"West Virginia University","ror":"https://ror.org/011vxgd24","country_code":"US","type":"education","lineage":["https://openalex.org/I12097938"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cun-Quan Zhang","raw_affiliation_strings":["Department of Mathematics, West Virginia University, Morgantown, WV 26506 USA"],"raw_orcid":"https://orcid.org/0000-0001-5583-4481","affiliations":[{"raw_affiliation_string":"Department of Mathematics, West Virginia University, Morgantown, WV 26506 USA","institution_ids":["https://openalex.org/I12097938"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1863,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.48984214,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"37","issue":"1","first_page":"253","last_page":"267"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9970999956130981,"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":0.9883999824523926,"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/conjecture","display_name":"Conjecture","score":0.7748250365257263},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7435348033905029},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7195907235145569},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5677809715270996},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5355318188667297},{"id":"https://openalex.org/keywords/cubic-graph","display_name":"Cubic graph","score":0.5309336185455322},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3962276577949524},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.13334059715270996},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0779276192188263},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.04968106746673584}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7748250365257263},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7435348033905029},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7195907235145569},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5677809715270996},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5355318188667297},{"id":"https://openalex.org/C100500283","wikidata":"https://www.wikidata.org/wiki/Q1374495","display_name":"Cubic graph","level":5,"score":0.5309336185455322},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3962276577949524},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.13334059715270996},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0779276192188263},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.04968106746673584}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1472425","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/22m1472425","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1949173501","display_name":"\u7f51\u7edc\u5bb9\u9519\u5d4c\u5165\u548c\u6545\u969c\u8bca\u65ad\u7814\u7a76","funder_award_id":"11971054","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2635788629","display_name":null,"funder_award_id":"11731002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3042492266","display_name":null,"funder_award_id":"DMS-1700218","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5178712706","display_name":null,"funder_award_id":"839830","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W92623642","https://openalex.org/W1543349373","https://openalex.org/W1855875669","https://openalex.org/W1964275362","https://openalex.org/W1964324196","https://openalex.org/W1977492432","https://openalex.org/W1994493716","https://openalex.org/W2022190032","https://openalex.org/W2022795828","https://openalex.org/W2049716158","https://openalex.org/W2073039945","https://openalex.org/W2077999329","https://openalex.org/W2091169105","https://openalex.org/W2165273484","https://openalex.org/W2202391886","https://openalex.org/W2314361409","https://openalex.org/W2332265223","https://openalex.org/W3082738679","https://openalex.org/W3084987570"],"related_works":["https://openalex.org/W3194471551","https://openalex.org/W4375956809","https://openalex.org/W1581373162","https://openalex.org/W2784911598","https://openalex.org/W4297950433","https://openalex.org/W4287023968","https://openalex.org/W4288279572","https://openalex.org/W1973978937","https://openalex.org/W4286909116","https://openalex.org/W2037002007"],"abstract_inverted_index":{".It":[0],"is":[1,22,111],"conjectured":[2],"that":[3,17,36],"every":[4,37],"bridgeless":[5,38],"graph":[6,39],"\\(G\\)":[7,21],"has":[8,40],"a":[9,32,41,70,92,96,100],"family":[10],"\\(\\mathcal{F}\\)":[11,29],"of":[12,20,28,105,116],"even":[13],"subgraphs":[14],"(cycles)":[15],"such":[16],"each":[18],"edge":[19],"contained":[23],"in":[24],"precisely":[25],"two":[26,80],"members":[27],"(CDC),":[30],"and":[31,50,82],"stronger":[33],"conjecture":[34,110],"says":[35],"5-even":[42],"subgraph":[43],"double":[44,118],"cover":[45],"(5-CDC).":[46],"Both":[47],"the":[48,51,108],"CDC":[49],"5-CDC":[52,109],"conjectures":[53],"are":[54],"confirmed":[55],"for":[56,95,113],"cubic":[57],"graphs":[58],"with":[59,87],"oddness":[60],"at":[61],"most":[62],"4.":[63],"In":[64],"this":[65],"paper,":[66],"we":[67],"first":[68],"introduce":[69],"new":[71],"approach":[72],"related":[73],"to":[74,77,90,98],"nowhere-zero":[75],"4-flows":[76],"attack":[78],"these":[79],"conjectures,":[81],"then":[83],"apply":[84],"it":[85],"together":[86],"Catlin":[88],"reduction":[89],"present":[91],"sufficient":[93],"condition":[94],"superposition":[97],"have":[99],"5-CDC.":[101],"As":[102],"an":[103],"application":[104],"those":[106],"results,":[107],"verified":[112],"several":[114],"families":[115],"snarks.Keywordscycle":[117],"cover4-flowCatlin":[119],"reductionsuperpositionsnarkMSC":[120],"codes05C7005C2105C38":[121]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}