{"id":"https://openalex.org/W2136655358","doi":"https://doi.org/10.1137/151006329","title":"Vector Flows and Integer Flows","display_name":"Vector Flows and Integer Flows","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2136655358","doi":"https://doi.org/10.1137/151006329","mag":"2136655358"},"language":"en","primary_location":{"id":"doi:10.1137/151006329","is_oa":false,"landing_page_url":"https://doi.org/10.1137/151006329","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/A5100364988","display_name":"Yi Wang","orcid":"https://orcid.org/0000-0002-9095-6879"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yi Wang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113834335","display_name":"Jian Cheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jian Cheng","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":"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":4,"corresponding_author_ids":["https://openalex.org/A5100364988"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.08435482,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"29","issue":"4","first_page":"2166","last_page":"2178"},"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":0.9994000196456909,"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":0.9968000054359436,"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/mathematics","display_name":"Mathematics","score":0.8448959589004517},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7956080436706543},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6204192638397217},{"id":"https://openalex.org/keywords/unit-vector","display_name":"Unit vector","score":0.6105117201805115},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5474262833595276},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5395905375480652},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4680601954460144},{"id":"https://openalex.org/keywords/converse","display_name":"Converse","score":0.4542645812034607},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.4401733875274658},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37486109137535095},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14437347650527954},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1369577944278717}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8448959589004517},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7956080436706543},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6204192638397217},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.6105117201805115},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5474262833595276},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5395905375480652},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4680601954460144},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.4542645812034607},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.4401733875274658},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37486109137535095},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14437347650527954},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1369577944278717},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"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:10.1137/151006329","is_oa":false,"landing_page_url":"https://doi.org/10.1137/151006329","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1964553741","https://openalex.org/W1976047413","https://openalex.org/W2065274214","https://openalex.org/W2314361409"],"related_works":["https://openalex.org/W2387449261","https://openalex.org/W2418518962","https://openalex.org/W2963377682","https://openalex.org/W2043159103","https://openalex.org/W2391769344","https://openalex.org/W2370553949","https://openalex.org/W4297833975","https://openalex.org/W2934154379","https://openalex.org/W2052067742","https://openalex.org/W2953384352"],"abstract_inverted_index":{"A":[0],"vector":[1,47,73,100,175,192],"${S}^d$-flow":[2],"is":[3,15,93,106,130,184],"a":[4,43,46,52,69,72,79,85,99,167,174],"flow":[5,7,140,155],"whose":[6],"values":[8],"are":[9,188],"vectors":[10,21,118],"in":[11,22],"$S^d$,":[12],"where":[13,128],"$S^d$":[14],"the":[16,91,109,131,134,147,153],"set":[17],"of":[18,87,98,111,136,149],"all":[19,116,124],"unit":[20],"$\\mathbb{R}^{d+1}$.":[23],"Jain":[24],"[Open":[25],"Problem":[26],"Garden,":[27],"http://www.openproblemgarden.org/op/unit_vector_flows":[28],"(2007)]":[29],"and":[30,83,146],"Thomassen":[31,56],"[J.":[32,57],"Combin.":[33,58],"Theory":[34,59],"Ser.":[35,60],"B.,":[36,61],"108":[37,62],"(2014),":[38,63],"pp.":[39,64],"81--91]":[40,65],"proved":[41],"that":[42,68,90,164,190],"graph":[44,70],"has":[45,51],"$S^1$-flow":[48,74,101],"if":[49,171],"it":[50],"nowhere-zero":[53,80,168,201],"integer":[54,81,169,202],"3-flow.":[55],"pointed":[66],"out":[67],"admitting":[71],"may":[75],"not":[76,94],"necessarily":[77],"admit":[78,191],"3-flow":[82,170],"presented":[84],"family":[86],"examples":[88,189],"showing":[89],"converse":[92],"true.":[95],"The":[96],"rank":[97,110,178,195],"$(":[102],"D,\\bm":[103],"{f}":[104],")$":[105],"defined":[107],"as":[108],"linear":[112],"space":[113],"generated":[114],"by":[115],"balanced":[117],"${\\bm{\\epsilon}}(v)=(\\epsilon_1(v),":[119],"\\epsilon_2(v),":[120],"\\ldots,":[121],"\\epsilon_b(v))$":[122],"for":[123],"$v":[125],"\\in":[126],"V(G)$,":[127],"$\\epsilon_i(v)$":[129],"difference":[132],"between":[133],"number":[135,148],"outgoing":[137],"edges":[138,151],"with":[139,152,177,194],"value":[141,156],"${\\bm":[142],"\\alpha}_i$":[143],"from":[144],"$v$":[145],"ingoing":[150],"same":[154],"to":[157],"$v$.":[158],"In":[159],"this":[160],"paper,":[161],"we":[162],"prove":[163],"$G$":[165,172],"admits":[166,173],"$S^{1}$-flow":[176],"at":[179,196],"most":[180],"two.":[181],"This":[182],"result":[183],"sharp":[185],"since":[186],"there":[187],"$S^1$-flows":[193],"least":[197],"3,":[198],"but":[199],"no":[200],"3-flows.":[203]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
