{"id":"https://openalex.org/W3135522219","doi":"https://doi.org/10.1137/20m1317141","title":"Integer Flows and Modulo Orientations of Signed Graphs","display_name":"Integer Flows and Modulo Orientations of Signed Graphs","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3135522219","doi":"https://doi.org/10.1137/20m1317141","mag":"3135522219"},"language":"en","primary_location":{"id":"doi:10.1137/20m1317141","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1317141","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/A5025543820","display_name":"Miaomiao Han","orcid":"https://orcid.org/0000-0001-7448-0930"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Miaomiao Han","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072223743","display_name":"Jiaao Li","orcid":"https://orcid.org/0000-0002-4771-2094"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiaao Li","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066405314","display_name":"Rong Luo","orcid":"https://orcid.org/0000-0002-5237-1001"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rong Luo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062762366","display_name":"Yongtang Shi","orcid":"https://orcid.org/0000-0001-9406-7967"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yongtang Shi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5064703404","display_name":"Cun\u2010Quan Zhang","orcid":"https://orcid.org/0000-0001-5583-4481"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cun-Quan Zhang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5025543820"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.05997007,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"35","issue":"1","first_page":"376","last_page":"391"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9994000196456909,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9962000250816345,"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/modulo","display_name":"Modulo","score":0.8787140846252441},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8100678324699402},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7491257190704346},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6936466693878174},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6858023405075073},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5704098343849182},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5320165157318115},{"id":"https://openalex.org/keywords/signed-graph","display_name":"Signed graph","score":0.5029587149620056},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.49004852771759033},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44601020216941833},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05417609214782715},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.04808470606803894}],"concepts":[{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.8787140846252441},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8100678324699402},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7491257190704346},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6936466693878174},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6858023405075073},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5704098343849182},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5320165157318115},{"id":"https://openalex.org/C2779773260","wikidata":"https://www.wikidata.org/wiki/Q11246292","display_name":"Signed graph","level":3,"score":0.5029587149620056},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.49004852771759033},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44601020216941833},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05417609214782715},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.04808470606803894},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1317141","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1317141","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/G1444980065","display_name":null,"funder_award_id":"11922112","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/G3946558102","display_name":null,"funder_award_id":"11901434","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5788347223","display_name":null,"funder_award_id":"11901318","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5840061355","display_name":null,"funder_award_id":"20JCZDJC00840","funder_id":"https://openalex.org/F4320323993","funder_display_name":"Natural Science Foundation of Tianjin City"},{"id":"https://openalex.org/G8059180067","display_name":null,"funder_award_id":"5RL159","funder_id":"https://openalex.org/F4320324792","funder_display_name":"Tianjin Normal University"},{"id":"https://openalex.org/G8910524701","display_name":null,"funder_award_id":"20JCJQJC00090","funder_id":"https://openalex.org/F4320323993","funder_display_name":"Natural Science Foundation of Tianjin City"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323021","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75"},{"id":"https://openalex.org/F4320323993","display_name":"Natural Science Foundation of Tianjin City","ror":null},{"id":"https://openalex.org/F4320324792","display_name":"Tianjin Normal University","ror":"https://ror.org/05x2td559"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W196573717","https://openalex.org/W1786780942","https://openalex.org/W1964553741","https://openalex.org/W2018784326","https://openalex.org/W2032431189","https://openalex.org/W2039779720","https://openalex.org/W2068987903","https://openalex.org/W2075527133","https://openalex.org/W2078014870","https://openalex.org/W2087420573","https://openalex.org/W2088648195","https://openalex.org/W2090562334","https://openalex.org/W2095645574","https://openalex.org/W2105800562","https://openalex.org/W2167804572","https://openalex.org/W2314361409","https://openalex.org/W2782589693","https://openalex.org/W2963010290","https://openalex.org/W3036546585","https://openalex.org/W3094302445","https://openalex.org/W4230039044","https://openalex.org/W4246110625","https://openalex.org/W4256646394"],"related_works":["https://openalex.org/W2117548279","https://openalex.org/W2807449856","https://openalex.org/W238211858","https://openalex.org/W2070252991","https://openalex.org/W2025727968","https://openalex.org/W2941201715","https://openalex.org/W2803761277","https://openalex.org/W2196131019","https://openalex.org/W2112041331","https://openalex.org/W4327715695"],"abstract_inverted_index":{"This":[0],"paper":[1,128],"studies":[2],"the":[3,35,40,100,107],"fundamental":[4,63],"relations":[5],"among":[6],"integer":[7,54],"flows,":[8,15],"modulo":[9,42],"orientations,":[10],"integer-valued":[11,48,86,111],"and":[12,16,80,93,135],"real-valued":[13],"circular":[14,104],"monotonicity":[17],"of":[18,65,102,109],"flows":[19],"in":[20,56,121,126],"signed":[21,68,75,98,131],"graphs.":[22],"A":[23],"(signed)":[24],"graph":[25,76],"is":[26,37,50,77,124],"modulo-$(2p+1)$-orientable":[27,78],"if":[28,79,82,133],"it":[29,83,123],"has":[30,118],"an":[31,85,110],"orientation":[32],"such":[33],"that":[34,72],"indegree":[36],"congruent":[38],"to":[39,67],"outdegree":[41],"$2p+1$":[43],"at":[44],"each":[45],"vertex.":[46],"An":[47],"$\\frac{2p+1}{p}$-flow":[49],"a":[51,62,73,103],"flow":[52],"taking":[53],"values":[55],"$\\{\\pm":[57],"p,":[58],"\\pm":[59],"(p+1)\\}$.":[60],"Extending":[61],"result":[64],"Jaeger":[66],"graphs,":[69],"we":[70],"show":[71],"bridgeless":[74,130],"only":[81],"admits":[84],"$\\frac{2p+1}{p}$-flow.":[87],"It":[88],"was":[89],"conjectured":[90],"by":[91],"Raspaud":[92],"Zhu":[94],"that,":[95],"for":[96,129],"any":[97],"graph,":[99],"admission":[101,108],"$r$-flow":[105],"implies":[106],"$\\lceil":[112],"r":[113],"\\rceil$-flow.":[114],"Although":[115],"this":[116,127],"conjecture":[117],"been":[119],"disproved":[120],"general,":[122],"confirmed":[125],"graphs":[132],"$r=\\frac{2p+1}{p}$":[134],"$p":[136],"\\geq":[137],"3$.":[138]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
