{"id":"https://openalex.org/W2964005335","doi":"https://doi.org/10.48550/arxiv.1205.0130","title":"On one-sided interval edge colorings of biregular bipartite graphs","display_name":"On one-sided interval edge colorings of biregular bipartite graphs","publication_year":2012,"publication_date":"2012-05-01","ids":{"openalex":"https://openalex.org/W2964005335","doi":"https://doi.org/10.48550/arxiv.1205.0130","mag":"2964005335"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1205.0130","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1205.0130","pdf_url":"https://arxiv.org/pdf/1205.0130","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1205.0130","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032006811","display_name":"Rafayel R. Kamalian","orcid":"https://orcid.org/0000-0003-4338-8466","observed_orcids":["https://orcid.org/0000-0003-4338-8466"]},"institutions":[{"id":"https://openalex.org/I4210133484","display_name":"Institute for Informatics and Automation Problems","ror":"https://ror.org/04a8k4p47","country_code":"AM","type":"facility","lineage":["https://openalex.org/I4210133484","https://openalex.org/I99064381"]},{"id":"https://openalex.org/I99064381","display_name":"National Academy of Sciences of Armenia","ror":"https://ror.org/04mczx267","country_code":"AM","type":"government","lineage":["https://openalex.org/I99064381"]}],"countries":["AM"],"is_corresponding":true,"raw_author_name":"Kamalian, R. R.","raw_affiliation_strings":["Institute for Informatics and Automation Problems , National Academy of Sciences of RA , 0014 Yerevan , Republic of Armenia","Institute for Informatics and Automation Problems of the National Academy of Sciences of RA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Informatics and Automation Problems , National Academy of Sciences of RA , 0014 Yerevan , Republic of Armenia","institution_ids":["https://openalex.org/I4210133484","https://openalex.org/I99064381"]},{"raw_affiliation_string":"Institute for Informatics and Automation Problems of the National Academy of Sciences of RA","institution_ids":["https://openalex.org/I4210133484"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5032006811"],"corresponding_institution_ids":["https://openalex.org/I4210133484","https://openalex.org/I99064381"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9887999892234802,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9887999892234802,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.009800000116229057,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":9.999999747378752e-05,"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/edge-coloring","display_name":"edge coloring","score":0.718999981880188},{"id":"https://openalex.org/keywords/edge-chromatic-number","display_name":"edge chromatic number","score":0.6269999742507935},{"id":"https://openalex.org/keywords/bipartite-graphs","display_name":"bipartite graphs","score":0.8539999723434448}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9024800062179565},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7616480588912964},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.7249699234962463},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.682294487953186},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.599068284034729},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5049141049385071},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46745094656944275},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.44871973991394043},{"id":"https://openalex.org/C21642379","wikidata":"https://www.wikidata.org/wiki/Q3342988","display_name":"Complete coloring","level":5,"score":0.4129534065723419},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.27693718671798706},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.11364036798477173}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:1205.0130","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1205.0130","pdf_url":"https://arxiv.org/pdf/1205.0130","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"pmh:oai:dspace.nbuv.gov.ua:123456789/154262","doi":null,"is_oa":true,"landing_page_url":"http://dspace.nbuv.gov.ua/handle/123456789/154262","pdf_url":"http://dspace.nbuv.gov.ua/handle/123456789/154262","source":{"id":"https://openalex.org/S4306401959","display_name":"The scientific electronic library of periodicals of the National Academy of Sciences of Ukraine (National Academy of Sciences of Ukraine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I149851306","host_organization_name":"National Academy of Sciences of Ukraine","host_organization_lineage":["https://openalex.org/I149851306"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"doi:10.48550/arxiv.1205.0130","doi":"https://doi.org/10.48550/arxiv.1205.0130","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1205.0130","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"mag:2964005335","doi":null,"is_oa":true,"landing_page_url":"http://admjournal.luguniv.edu.ua/index.php/adm/article/download/46/13","pdf_url":null,"source":{"id":"https://openalex.org/S4306501371","display_name":"Algebra and Discrete Mathematics","issn_l":"1726-3255","issn":["1726-3255","2415-721X"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-c","poland-40","russia-white-list-4"],"host_organization":"https://openalex.org/I2800458533","host_organization_name":"University of Luhansk","host_organization_lineage":["https://openalex.org/I2800458533"],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Algebra and Discrete Mathematics","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1205.0130","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1205.0130","pdf_url":"https://arxiv.org/pdf/1205.0130","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2964005335.pdf","grobid_xml":"https://content.openalex.org/works/W2964005335.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W164191045","https://openalex.org/W1479863711","https://openalex.org/W1553957963","https://openalex.org/W2018072810","https://openalex.org/W2040404838","https://openalex.org/W2051167419","https://openalex.org/W2082689120","https://openalex.org/W2086780347","https://openalex.org/W2097936723"],"related_works":["https://openalex.org/W2005967205","https://openalex.org/W581710347","https://openalex.org/W2595145913","https://openalex.org/W1851517242","https://openalex.org/W7096017535","https://openalex.org/W310380010","https://openalex.org/W579291033","https://openalex.org/W6995455738","https://openalex.org/W1804476206","https://openalex.org/W1651418664"],"abstract_inverted_index":{"A":[0],"proper":[1,65,90,136,172],"edge":[2,66,91,137,173],"$t$-coloring":[3,67,92,138,174],"of":[4,11,13,35,37,48,54,68,81,94,104,106,125,127,139,155,165,175,195,207,210,213],"a":[5,9,41,46,64,69,89,95,101,122,135,149,152,171],"graph":[6,70,96],"$G$":[7,14,71,97,128,140,147,176],"is":[8,44,57,72,83,98,115,134,142,148,170,180],"coloring":[10],"edges":[12,28,38],"with":[15,40,204],"colors":[16,21,36],"$1,2,...,t$":[17],"such":[18],"that":[19,63,88,121,199],"all":[20,208],"are":[22],"used,":[23],"and":[24,151],"no":[25],"two":[26],"adjacent":[27],"receive":[29],"the":[30,75,79,162,193,205,214],"same":[31],"color.":[32],"The":[33],"set":[34,206],"incident":[39],"vertex":[42,76],"$x$":[43,77,82],"called":[45,58],"spectrum":[47,80],"$x$.":[49,118],"An":[50],"arbitrary":[51,111],"nonempty":[52],"subset":[53,102,123,153],"consecutive":[55],"integers":[56],"an":[59,84,110,130,159],"interval.":[60,85],"We":[61,86,119],"say":[62,87,120],"interval":[73,99,116,143,177],"in":[74,117,198],"if":[78,108,132],"$\u03c6$":[93,114],"on":[100,144,178],"$R_0$":[103],"vertices":[105,126,157,209],"$G$,":[107],"for":[109,167,187],"$x\\in":[112],"R_0$,":[113],"$R$":[124,154,179,202],"has":[129,158],"$i$-property":[131],"there":[133,169],"which":[141,168],"$R$.":[145],"If":[146],"graph,":[150],"its":[156],"$i$-property,":[160],"then":[161],"minimum":[163],"value":[164,194],"$t$":[166],"denoted":[181],"by":[182],"$w_R(G)$.":[183],"In":[184],"this":[185,196],"paper,":[186],"some":[188],"bipartite":[189],"graphs,":[190],"we":[191],"estimate":[192],"parameter":[197],"cases":[200],"when":[201],"coincides":[203],"one":[211],"part":[212],"graph.":[215]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2019-07-30T00:00:00"}
