{"id":"https://openalex.org/W4378977652","doi":"https://doi.org/10.1137/22m1496529","title":"On Density of \\(\\boldsymbol{\\mathbb{Z}_3}\\) -Flow-Critical Graphs","display_name":"On Density of \\(\\boldsymbol{\\mathbb{Z}_3}\\) -Flow-Critical Graphs","publication_year":2023,"publication_date":"2023-06-01","ids":{"openalex":"https://openalex.org/W4378977652","doi":"https://doi.org/10.1137/22m1496529"},"language":"en","primary_location":{"id":"doi:10.1137/22m1496529","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1496529","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/A5073630443","display_name":"Zden\u0115k Dvo\u0159\u00e1k","orcid":null},"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"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Zden\u011bk Dvo\u0159\u00e1k","raw_affiliation_strings":["Computer Science Institute CSI of Charles University, Malostransk\u00e9 n\u00e1m\u011bst\u00ed 25, 118 00 Prague, Czech Republic"],"raw_orcid":"https://orcid.org/0000-0002-8308-9746","affiliations":[{"raw_affiliation_string":"Computer Science Institute CSI of Charles University, Malostransk\u00e9 n\u00e1m\u011bst\u00ed 25, 118 00 Prague, Czech Republic","institution_ids":["https://openalex.org/I21250087"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005993212","display_name":"Bojan Mohar","orcid":"https://orcid.org/0000-0002-7408-6148"},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Bojan Mohar","raw_affiliation_strings":["Department of Mathematics, Simon Fraser University Burnaby, BC V5A 1S6 Canada. On leave from IMFM & FMF, Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia"],"raw_orcid":"https://orcid.org/0000-0002-7408-6148","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Simon Fraser University Burnaby, BC V5A 1S6 Canada. On leave from IMFM & FMF, Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia","institution_ids":["https://openalex.org/I18014758"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073630443"],"corresponding_institution_ids":["https://openalex.org/I21250087"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11427908,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"37","issue":"2","first_page":"699","last_page":"717"},"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":0.9983000159263611,"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/T11476","display_name":"Graph theory and applications","score":0.9926000237464905,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.817916750907898},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.661537766456604},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5595768094062805},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5523914098739624},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.5164337754249573},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4413588345050812},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4393789768218994},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.4166056513786316},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16306567192077637},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11824551224708557}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.817916750907898},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.661537766456604},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5595768094062805},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5523914098739624},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5164337754249573},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4413588345050812},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4393789768218994},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.4166056513786316},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16306567192077637},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11824551224708557}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1496529","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1496529","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/G1044547","display_name":null,"funder_award_id":"J1-2452","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G1938958468","display_name":null,"funder_award_id":"22-17398S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G548662704","display_name":null,"funder_award_id":"R611450","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"},{"id":"https://openalex.org/F4320322554","display_name":"Javna Agencija za Raziskovalno Dejavnost RS","ror":"https://ror.org/059bp8k51"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W223802390","https://openalex.org/W1973134740","https://openalex.org/W1976047413","https://openalex.org/W1978379258","https://openalex.org/W1982423514","https://openalex.org/W1998391578","https://openalex.org/W2002164745","https://openalex.org/W2018810952","https://openalex.org/W2023859733","https://openalex.org/W2071623897","https://openalex.org/W2088648195","https://openalex.org/W2120821287","https://openalex.org/W2140381653","https://openalex.org/W2148392390","https://openalex.org/W2154145620","https://openalex.org/W2314361409","https://openalex.org/W2962855779","https://openalex.org/W2970481648","https://openalex.org/W3208850741","https://openalex.org/W4231473828","https://openalex.org/W4253136899"],"related_works":["https://openalex.org/W2378598099","https://openalex.org/W2611275940","https://openalex.org/W2367539883","https://openalex.org/W4206878504","https://openalex.org/W2324609820","https://openalex.org/W15871775","https://openalex.org/W1606013690","https://openalex.org/W4293743430","https://openalex.org/W3006156235","https://openalex.org/W2073591271"],"abstract_inverted_index":{"For":[0],"an":[1],"abelian":[2],"group":[3],",":[4,23],"a":[5,16,27,32,42],"graph":[6],"is":[7],"said":[8],"to":[9],"be":[10],"-flow-critical":[11,38],"if":[12],"does":[13],"not":[14],"admit":[15],"nowhere-zero":[17,28],"-flow,":[18],"but":[19],"for":[20],"each":[21],"edge":[22],"the":[24,35,46,50,53],"contraction":[25],"has":[26],"-flow.":[29],"We":[30],"obtain":[31],"bound":[33,51],"on":[34,41,52],"density":[36,54],"of":[37,49,55],"graphs":[39,57],"drawn":[40],"fixed":[43],"surface,":[44],"generalizing":[45],"planar":[47],"case":[48],"4-critical":[56],"by":[58],"Kostochka":[59],"and":[60],"Yancey.":[61]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}