{"id":"https://openalex.org/W4389581326","doi":"https://doi.org/10.1142/s1793830923501094","title":"Fractional coloring problem of 1-planar graphs without short cycles","display_name":"Fractional coloring problem of 1-planar graphs without short cycles","publication_year":2023,"publication_date":"2023-12-12","ids":{"openalex":"https://openalex.org/W4389581326","doi":"https://doi.org/10.1142/s1793830923501094"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830923501094","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830923501094","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","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/A5102009599","display_name":"Mengjiao Li","orcid":"https://orcid.org/0000-0003-4801-560X"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Meng Jiao Li","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, P. R. China","institution_ids":["https://openalex.org/I28006308"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100716519","display_name":"Lei Sun","orcid":"https://orcid.org/0000-0002-5050-7630"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lei Sun","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-5050-7630","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, P. R. China","institution_ids":["https://openalex.org/I28006308"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016946533","display_name":"Wei Zheng","orcid":"https://orcid.org/0000-0003-2377-7544"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Zheng","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, P. R. China","institution_ids":["https://openalex.org/I28006308"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100716519"],"corresponding_institution_ids":["https://openalex.org/I28006308"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.28390021,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"08","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.8493000268936157,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.8493000268936157,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.8220999836921692,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.742900013923645,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6172084808349609},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.5646752715110779},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48699766397476196},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44285863637924194},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36739596724510193},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2046138346195221},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.1275174915790558}],"concepts":[{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6172084808349609},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.5646752715110779},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48699766397476196},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44285863637924194},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36739596724510193},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2046138346195221},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.1275174915790558}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830923501094","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830923501094","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5497508197","display_name":null,"funder_award_id":"ZR202102250232","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G6171926925","display_name":null,"funder_award_id":"12271331","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6659929261","display_name":null,"funder_award_id":"12071265","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W2054273854","https://openalex.org/W2059488568","https://openalex.org/W2092084263","https://openalex.org/W2948783856","https://openalex.org/W2963971110","https://openalex.org/W2964094665","https://openalex.org/W3015759841","https://openalex.org/W3092377632","https://openalex.org/W4210799492","https://openalex.org/W4232896595"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3216105633","https://openalex.org/W1701875187","https://openalex.org/W2990956612"],"abstract_inverted_index":{"We":[0],"consider":[1,146],"a":[2,9,24,47,88],"new":[3],"coloring":[4],"as":[5],"follows":[6],"such":[7,130],"that":[8,90,131,176],"subset":[10,49],"of":[11,50,96,106,116,126,155],"[Formula:":[12,20,29,33,40,43,51,55,62,65,70,83,93,97,102,107,113,117,122,127,148,151,156,178,183,186,191,195,198,203],"see":[13,21,30,34,41,44,52,56,63,66,71,84,94,98,103,108,114,118,123,128,149,152,157,179,184,187,192,196,199,204],"text]":[14,22,31,35,45,57,95,99,104,109,115,119,124,129],"needs":[15],"very":[16],"few":[17],"colors.":[18],"Let":[19],"be":[23,36,61,77],"graph":[25,54,181],"with":[26,39],"vertex":[27,48,92,112],"set":[28,69,202],"and":[32,110,163,189],"three":[37],"integers":[38],"text].":[42,205],"is":[46,58,87,100,120,194],"text],":[53,72,85],"said":[59],"to":[60,136],"text]-weak":[64,150,197],"text]-choosable":[67,153,200],"about":[68,201],"if":[73],"the":[74,132,147,168],"following":[75],"can":[76],"satisfied:":[78],"For":[79],"any":[80],"list":[81],"assignment":[82],"there":[86],"way":[89],"each":[91,111],"assigned":[101,121],"colors":[105,125],"color":[133],"sets":[134],"corresponding":[135],"adjacent":[137,190],"vertices":[138],"do":[139],"not":[140],"intersect.":[141],"In":[142,171],"this":[143,172],"paper,":[144,173],"we":[145,174],"problem":[154],"text]-planar":[158,180],"graphs":[159],"without":[160,182],"short":[161],"cycles":[162],"prove":[164,175],"our":[165],"results":[166],"by":[167],"discharging":[169],"method.":[170],"every":[177],"text]-cycles,":[185],"text]-cycles":[188,193]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
