{"id":"https://openalex.org/W1972024351","doi":"https://doi.org/10.1155/2013/380861","title":"Some Conclusion on Unique<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:math>-List Colorable Complete Multipartite Graphs","display_name":"Some Conclusion on Unique<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:math>-List Colorable Complete Multipartite Graphs","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1972024351","doi":"https://doi.org/10.1155/2013/380861","mag":"1972024351"},"language":"lv","primary_location":{"id":"doi:10.1155/2013/380861","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/380861","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/380861.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2013/380861.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101740515","display_name":"Yanning Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]},{"id":"https://openalex.org/I4210128819","display_name":"Institute of Electrical Engineering","ror":"https://ror.org/033js6g46","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128819"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanning Wang","raw_affiliation_strings":["Key Lab of Industrial Computer Control Engineering of Hebei Province, Institute of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei 066004, China","School of Economics and Management, Yanshan University, Qinhuangdao, Hebei 066004, China","School of Sciences, Yanshan University, Qinhuangdao, Hebei 066004, China"],"affiliations":[{"raw_affiliation_string":"Key Lab of Industrial Computer Control Engineering of Hebei Province, Institute of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei 066004, China","institution_ids":["https://openalex.org/I39333907","https://openalex.org/I4210128819"]},{"raw_affiliation_string":"School of Economics and Management, Yanshan University, Qinhuangdao, Hebei 066004, China","institution_ids":["https://openalex.org/I39333907"]},{"raw_affiliation_string":"School of Sciences, Yanshan University, Qinhuangdao, Hebei 066004, China","institution_ids":["https://openalex.org/I39333907"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100388809","display_name":"Yanyan Wang","orcid":"https://orcid.org/0000-0001-9730-6871"},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]},{"id":"https://openalex.org/I4210128819","display_name":"Institute of Electrical Engineering","ror":"https://ror.org/033js6g46","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128819"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanyan Wang","raw_affiliation_strings":["Key Lab of Industrial Computer Control Engineering of Hebei Province, Institute of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei 066004, China","School of Economics and Management, Yanshan University, Qinhuangdao, Hebei 066004, China","School of Sciences, Yanshan University, Qinhuangdao, Hebei 066004, China"],"affiliations":[{"raw_affiliation_string":"Key Lab of Industrial Computer Control Engineering of Hebei Province, Institute of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei 066004, China","institution_ids":["https://openalex.org/I39333907","https://openalex.org/I4210128819"]},{"raw_affiliation_string":"School of Economics and Management, Yanshan University, Qinhuangdao, Hebei 066004, China","institution_ids":["https://openalex.org/I39333907"]},{"raw_affiliation_string":"School of Sciences, Yanshan University, Qinhuangdao, Hebei 066004, China","institution_ids":["https://openalex.org/I39333907"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100709503","display_name":"Xuguang Zhang","orcid":"https://orcid.org/0000-0001-7029-3484"},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]},{"id":"https://openalex.org/I4210128819","display_name":"Institute of Electrical Engineering","ror":"https://ror.org/033js6g46","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128819"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xuguang Zhang","raw_affiliation_strings":["Key Lab of Industrial Computer Control Engineering of Hebei Province, Institute of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei 066004, China"],"affiliations":[{"raw_affiliation_string":"Key Lab of Industrial Computer Control Engineering of Hebei Province, Institute of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei 066004, China","institution_ids":["https://openalex.org/I39333907","https://openalex.org/I4210128819"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100709503"],"corresponding_institution_ids":["https://openalex.org/I39333907","https://openalex.org/I4210128819"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.3699,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.62134202,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9980999827384949,"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":0.9980999827384949,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9927999973297119,"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/T11409","display_name":"Advanced Wireless Network Optimization","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/algorithm","display_name":"Algorithm","score":0.5980492830276489},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.37150198221206665},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3625410795211792}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5980492830276489},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.37150198221206665},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3625410795211792}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2013/380861","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/380861","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/380861.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1394808157","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1394808157","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:beb4b24ff36640af82b78a8e56741e66","is_oa":true,"landing_page_url":"https://doaj.org/article/beb4b24ff36640af82b78a8e56741e66","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/380861","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/380861","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/380861.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1121271761","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1467724465","display_name":null,"funder_award_id":"2013T60264","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G2082826544","display_name":null,"funder_award_id":"Postdoctoral","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5086537808","display_name":null,"funder_award_id":"61271409","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5183505615","display_name":null,"funder_award_id":"2012M510768","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5385568429","display_name":null,"funder_award_id":"201001A151","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G5469106741","display_name":null,"funder_award_id":"2012M","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G5939423041","display_name":null,"funder_award_id":"Technology","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6058138561","display_name":null,"funder_award_id":", No.","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6642528675","display_name":null,"funder_award_id":"61271409","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G6723228526","display_name":null,"funder_award_id":"2012M510768","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G6948383776","display_name":null,"funder_award_id":"2013T60264","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6979334471","display_name":null,"funder_award_id":"201001A151","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/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1972024351.pdf","grobid_xml":"https://content.openalex.org/works/W1972024351.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W116172775","https://openalex.org/W1505443956","https://openalex.org/W1538135112","https://openalex.org/W1658964660","https://openalex.org/W2049904819","https://openalex.org/W2056065955","https://openalex.org/W2123506360","https://openalex.org/W2126105838","https://openalex.org/W2142340436","https://openalex.org/W2170991283","https://openalex.org/W2355076164","https://openalex.org/W2753881962","https://openalex.org/W2963385493"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2530322880"],"abstract_inverted_index":{"If":[0],"a":[1,14,94,104,115],"graph<mml:math":[2,83],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[3,6,9,12,16,19,23,29,40,47,64,68,84,90,109,112,131],"id=\"M2\"><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>admits":[4],"a<mml:math":[5],"id=\"M3\"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:math>-list":[7],"assignment<mml:math":[8],"id=\"M4\"><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:math>such":[10],"that<mml:math":[11],"id=\"M5\"><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>has":[13],"unique<mml:math":[15,63],"id=\"M6\"><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:math>-coloring,":[17],"then<mml:math":[18],"id=\"M7\"><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>is":[20],"called":[21],"uniquely<mml:math":[22],"id=\"M8\"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:math>-list":[24],"colorable":[25],"graph,":[26],"or":[27],"U<mml:math":[28,39,89,108,130],"id=\"M9\"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:math>LC":[30],"graph":[31],"for":[32,98],"short.":[33],"In":[34,71],"the":[35,43,62,79,82,126],"process":[36],"of":[37,81,107,117],"characterizing":[38],"id=\"M10\"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:math>LC":[41],"graphs,":[42],"complete":[44,133],"multipartite":[45,134],"graphs<mml:math":[46,111],"id=\"M11\"><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mi":[48],"mathvariant=\"normal\">*</mml:mi><mml:mi>r</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo":[49],"stretchy=\"false\">(</mml:mo><mml:mi>r</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi><mml:mo>\u2208</mml:mo><mml:mi>N</mml:mi><mml:mo":[50],"stretchy=\"false\">)</mml:mo></mml:math>are":[51],"often":[52],"researched.":[53],"But":[54],"it":[55,87],"is":[56,88,120],"usually":[57],"not":[58],"easy":[59],"to":[60,128],"construct":[61],"id=\"M12\"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:math>-list":[65],"assignment":[66],"of<mml:math":[67],"id=\"M13\"><mml:mrow><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mi":[69],"mathvariant=\"normal\">*</mml:mi><mml:mi>r</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>.":[70],"this":[72],"paper,":[73],"we":[74],"give":[75],"some":[76],"propositions":[77,119],"about":[78],"property":[80],"id=\"M14\"><mml:mrow><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mi":[85],"mathvariant=\"normal\">*</mml:mi><mml:mi>r</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>when":[86],"id=\"M15\"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:math>LC,":[91],"which":[92],"provide":[93],"very":[95],"significant":[96],"guide":[97],"constructing":[99],"such":[100],"list":[101],"assignment.":[102],"Then":[103],"special":[105],"example":[106],"id=\"M16\"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:math>LC":[110],"id=\"M17\"><mml:mrow><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mi":[113],"mathvariant=\"normal\">*</mml:mi><mml:mi>r</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>as":[114],"application":[116],"these":[118],"introduced.":[121],"The":[122],"conclusion":[123],"will":[124],"pave":[125],"way":[127],"characterize":[129],"id=\"M18\"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:math>LC":[132],"graphs.":[135]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2016-06-24T00:00:00"}
