{"id":"https://openalex.org/W2296003088","doi":"https://doi.org/10.4086/toc.2012.v008a025","title":"","display_name":"","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2296003088","doi":"https://doi.org/10.4086/toc.2012.v008a025","mag":"2296003088"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2012.v008a025","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2012.v008a025","pdf_url":"https://theoryofcomputing.org/articles/v008a025/v008a025.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://theoryofcomputing.org/articles/v008a025/v008a025.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074192084","display_name":"Bahman Bahmani","orcid":"https://orcid.org/0000-0001-5485-3314"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bahman Bahmani","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075894805","display_name":"Aranyak Mehta","orcid":"https://orcid.org/0000-0002-6132-4901"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aranyak Mehta","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5112649653","display_name":"Rajeev Motwani","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rajeev Motwani","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3631,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.67895399,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"8","issue":"1","first_page":"567","last_page":"595"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T12288","display_name":"Optimization and Search Problems","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9993000030517578,"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":0.9991999864578247,"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/combinatorics","display_name":"Combinatorics","score":0.7819416522979736},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5056133270263672},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.49909281730651855},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.497548371553421},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.4930400550365448},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.480365127325058},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.4395330846309662},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.43389222025871277},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.39680248498916626},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.24808862805366516},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.13035848736763}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7819416522979736},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5056133270263672},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.49909281730651855},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.497548371553421},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.4930400550365448},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.480365127325058},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.4395330846309662},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.43389222025871277},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.39680248498916626},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.24808862805366516},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.13035848736763},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4086/toc.2012.v008a025","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2012.v008a025","pdf_url":"https://theoryofcomputing.org/articles/v008a025/v008a025.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4086/toc.2012.v008a025","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2012.v008a025","pdf_url":"https://theoryofcomputing.org/articles/v008a025/v008a025.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2296003088.pdf","grobid_xml":"https://content.openalex.org/works/W2296003088.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1965765215","https://openalex.org/W1971663478","https://openalex.org/W1986826668","https://openalex.org/W1989274820","https://openalex.org/W2052354487","https://openalex.org/W2082903339","https://openalex.org/W2102669784","https://openalex.org/W2165076510"],"related_works":["https://openalex.org/W238609530","https://openalex.org/W2734192830","https://openalex.org/W3016395638","https://openalex.org/W1636163329","https://openalex.org/W4292947165","https://openalex.org/W3045121788","https://openalex.org/W3127082728","https://openalex.org/W2067936666","https://openalex.org/W2016190491","https://openalex.org/W2907832623"],"abstract_inverted_index":{"A":[0,49,101],"classic":[1],"theorem":[2],"by":[3,72,217,231],"Vizing":[4],"asserts":[5],"that":[6,105,181],"if":[7],"the":[8,42,60,64,67,88,116,120,129,133,141,158,172,193,209],"maximum":[9],"degree":[10],"of":[11,66,132,147,160,174,223],"a":[12,111,153,218],"graph":[13,44,68,194],"is":[14,18,36,45,53,85,104,128,171,189,215],",":[15],"then":[16,52],"it":[17,40,84,188],"possible":[19,190],"to":[20,77,87,191],"color":[21,78,192],"its":[22],"edges,":[23],"in":[24,47,59,97,110,115,140,208],"polynomial":[25],"time,":[26],"using":[27],"at":[28],"most":[29],"+":[30,197,201],"1":[31,196],"colors.":[32],"However,":[33],"this":[34,177],"algorithm":[35,127,136,146,156,214,222],"offline,":[37],"i.":[38],"e.,":[39],"assumes":[41],"whole":[43],"known":[46],"advance.":[48],"natural":[50,102],"question":[51],"how":[54],"well":[55],"we":[56,75,179,229],"can":[57],"do":[58],"online":[61,143,210],"setting,":[62],"where":[63,169],"edges":[65,106],"are":[69],"revealed":[70],"one":[71],"one,":[73],"and":[74,225],"need":[76],"each":[79],"edge":[80,91],"as":[81,83],"soon":[82],"added":[86],"graph.":[89],"Online":[90],"coloring":[92],"has":[93],"an":[94],"important":[95],"application":[96],"fast":[98],"switch":[99],"scheduling.":[100],"model":[103],"arrive":[107],"online,":[108],"but":[109],"random":[112,117],"permutation.":[113],"Even":[114],"permutation":[118],"model,":[119],"best":[121],"proven":[122],"approximation":[123],"factor":[124,130,155],"for":[125,157,182],"any":[126],"2":[131,167,199],"simple":[134],"greedy":[135],"(which":[137],"holds":[138],"even":[139],"worst-case":[142],"model).":[144],"The":[145],"Aggarwal":[148],"et":[149],"al.":[150],"(FOCS'03)":[151],"provides":[152],"1+o(1)":[154],"case":[159],"very":[161],"dense":[162],"multi-graphs,":[163],"when":[164],"=":[165,185],"(n":[166],"),":[168],"n":[170],"number":[173],"vertices.":[175],"In":[176],"paper,":[178],"show":[180],"graphs":[183],"with":[184,195,205],"(log":[186],"n),":[187],"e/(e":[198],"-1)":[200],"o(1)":[202],"1.43":[203],"colors,":[204],"high":[206],"probability,":[207],"random-order":[211],"model.":[212],"Our":[213],"inspired":[216],"1.6-approximate":[219],"distributed":[220],"offline":[221],"Panconesi":[224],"Srinivasan":[226],"(PODC'92),":[227],"which":[228],"extend":[230],"reusing":[232],"failed":[233],"colors":[234],"online.":[235]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-12-17T22:08:43.090829","created_date":"2016-06-24T00:00:00"}