{"id":"https://openalex.org/W4294770436","doi":"https://doi.org/10.1137/21m1447714","title":"Faster 3-Coloring of Small-Diameter Graphs","display_name":"Faster 3-Coloring of Small-Diameter Graphs","publication_year":2022,"publication_date":"2022-09-01","ids":{"openalex":"https://openalex.org/W4294770436","doi":"https://doi.org/10.1137/21m1447714"},"language":"en","primary_location":{"id":"doi:10.1137/21m1447714","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1447714","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/A5069681719","display_name":"Micha\u0142 D\u0229bsk","orcid":null},"institutions":[{"id":"https://openalex.org/I108403487","display_name":"Warsaw University of Technology","ror":"https://ror.org/00y0xnp53","country_code":"PL","type":"education","lineage":["https://openalex.org/I108403487"]},{"id":"https://openalex.org/I2799853480","display_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","ror":"https://ror.org/00k4h2615","country_code":"DE","type":"facility","lineage":["https://openalex.org/I2799853480","https://openalex.org/I315704651"]},{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["DE","PL"],"is_corresponding":false,"raw_author_name":"Micha\u0142 D\u0229bsk","raw_affiliation_strings":["Institute of Informatics, University of Warsaw, Poland","Faculty of Mathematics and Information Science, Warsaw University of Technology, Poland","Leibniz International Proceedings in Informatics Schloss Dagstuhl -Leibniz-Zentrum f\u00fcr Informatik, Dagstuhl Publishing, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Informatics, University of Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]},{"raw_affiliation_string":"Faculty of Mathematics and Information Science, Warsaw University of Technology, Poland","institution_ids":["https://openalex.org/I108403487"]},{"raw_affiliation_string":"Leibniz International Proceedings in Informatics Schloss Dagstuhl -Leibniz-Zentrum f\u00fcr Informatik, Dagstuhl Publishing, Germany","institution_ids":["https://openalex.org/I2799853480"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047929302","display_name":"Marta Piecyk","orcid":"https://orcid.org/0000-0001-9162-8300"},"institutions":[{"id":"https://openalex.org/I108403487","display_name":"Warsaw University of Technology","ror":"https://ror.org/00y0xnp53","country_code":"PL","type":"education","lineage":["https://openalex.org/I108403487"]},{"id":"https://openalex.org/I2799853480","display_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","ror":"https://ror.org/00k4h2615","country_code":"DE","type":"facility","lineage":["https://openalex.org/I2799853480","https://openalex.org/I315704651"]},{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["DE","PL"],"is_corresponding":false,"raw_author_name":"Marta Piecyk","raw_affiliation_strings":["Institute of Informatics, University of Warsaw, Poland","Faculty of Mathematics and Information Science, Warsaw University of Technology, Poland","Leibniz International Proceedings in Informatics Schloss Dagstuhl -Leibniz-Zentrum f\u00fcr Informatik, Dagstuhl Publishing, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Informatics, University of Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]},{"raw_affiliation_string":"Faculty of Mathematics and Information Science, Warsaw University of Technology, Poland","institution_ids":["https://openalex.org/I108403487"]},{"raw_affiliation_string":"Leibniz International Proceedings in Informatics Schloss Dagstuhl -Leibniz-Zentrum f\u00fcr Informatik, Dagstuhl Publishing, Germany","institution_ids":["https://openalex.org/I2799853480"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047941027","display_name":"Pawe\u0142 Rz\u0105\u017cewski","orcid":"https://orcid.org/0000-0001-7696-3848"},"institutions":[{"id":"https://openalex.org/I108403487","display_name":"Warsaw University of Technology","ror":"https://ror.org/00y0xnp53","country_code":"PL","type":"education","lineage":["https://openalex.org/I108403487"]},{"id":"https://openalex.org/I2799853480","display_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","ror":"https://ror.org/00k4h2615","country_code":"DE","type":"facility","lineage":["https://openalex.org/I2799853480","https://openalex.org/I315704651"]},{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["DE","PL"],"is_corresponding":false,"raw_author_name":"Pawe\u0142 Rza\u0327\u017cewski","raw_affiliation_strings":["Leibniz International Proceedings in Informatics Schloss Dagstuhl -Leibniz-Zentrum f\u00fcr Informatik, Dagstuhl Publishing, Germany","Institute of Informatics, University of Warsaw, Poland","Faculty of Mathematics and Information Science, Warsaw University of Technology, Poland"],"raw_orcid":"https://orcid.org/0000-0001-7696-3848","affiliations":[{"raw_affiliation_string":"Leibniz International Proceedings in Informatics Schloss Dagstuhl -Leibniz-Zentrum f\u00fcr Informatik, Dagstuhl Publishing, Germany","institution_ids":["https://openalex.org/I2799853480"]},{"raw_affiliation_string":"Institute of Informatics, University of Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]},{"raw_affiliation_string":"Faculty of Mathematics and Information Science, Warsaw University of Technology, Poland","institution_ids":["https://openalex.org/I108403487"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6632,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.7120307,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"36","issue":"3","first_page":"2205","last_page":"2224"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9857000112533569,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9857000112533569,"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":0.8252232074737549},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7355657815933228},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5532358884811401},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.536005973815918},{"id":"https://openalex.org/keywords/brooks-theorem","display_name":"Brooks' theorem","score":0.5093790292739868},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.5022287368774414},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.5014395713806152},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.483325719833374},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48327046632766724},{"id":"https://openalex.org/keywords/complete-coloring","display_name":"Complete coloring","score":0.47246360778808594},{"id":"https://openalex.org/keywords/greedy-coloring","display_name":"Greedy coloring","score":0.4347195327281952},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.4341574013233185},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.40088382363319397},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.1731431782245636},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.08055174350738525},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.05823001265525818}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8252232074737549},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7355657815933228},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5532358884811401},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.536005973815918},{"id":"https://openalex.org/C51658606","wikidata":"https://www.wikidata.org/wiki/Q512897","display_name":"Brooks' theorem","level":5,"score":0.5093790292739868},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.5022287368774414},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.5014395713806152},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.483325719833374},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48327046632766724},{"id":"https://openalex.org/C21642379","wikidata":"https://www.wikidata.org/wiki/Q3342988","display_name":"Complete coloring","level":5,"score":0.47246360778808594},{"id":"https://openalex.org/C38767284","wikidata":"https://www.wikidata.org/wiki/Q5601715","display_name":"Greedy coloring","level":5,"score":0.4347195327281952},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.4341574013233185},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.40088382363319397},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.1731431782245636},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.08055174350738525},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.05823001265525818}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1447714","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1447714","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/G7561358084","display_name":null,"funder_award_id":"2018/31/D/ST6/00062","funder_id":"https://openalex.org/F4320322511","funder_display_name":"Narodowe Centrum Nauki"}],"funders":[{"id":"https://openalex.org/F4320322511","display_name":"Narodowe Centrum Nauki","ror":"https://ror.org/03ha2q922"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1791386552","https://openalex.org/W1873654474","https://openalex.org/W1968069760","https://openalex.org/W1973199140","https://openalex.org/W1976802224","https://openalex.org/W1996763543","https://openalex.org/W2006753964","https://openalex.org/W2057826895","https://openalex.org/W2087858212","https://openalex.org/W2104062785","https://openalex.org/W2130481157","https://openalex.org/W2913141481","https://openalex.org/W2914414140","https://openalex.org/W2962956065","https://openalex.org/W2963110909","https://openalex.org/W2964258819","https://openalex.org/W2977322974","https://openalex.org/W3111025503","https://openalex.org/W3112807772","https://openalex.org/W3164098456","https://openalex.org/W4213009134"],"related_works":["https://openalex.org/W4311345810","https://openalex.org/W1542397451","https://openalex.org/W3169197204","https://openalex.org/W4297911588","https://openalex.org/W2380525562","https://openalex.org/W4229747356","https://openalex.org/W398688634","https://openalex.org/W2585997002","https://openalex.org/W2793500002","https://openalex.org/W4320918672"],"abstract_inverted_index":{"We":[0,171],"study":[1],"the":[2,33,47,74,78,85,95,105,112,157,179],"3-Coloring":[3,62,141,161],"problem":[4,22,34,106],"in":[5,26,38,46,63,67,84,145,151,164],"graphs":[6,20,66],"with":[7],"small":[8],"diameter.":[9],"In":[10,53,98],"2013,":[11],"Mertzios":[12,81],"and":[13,82,103],"Spirakis":[14,83],"showed":[15],"that":[16,60,140],"for":[17,160,167],"$n$-vertex":[18,64,152],"diameter-2":[19,65,125],"this":[21,54],"can":[23,35,142],"be":[24,36,143],"solved":[25,37,144],"subexponential":[27,165],"time":[28,40,68,146,166],"$2^{\\mathcal{O}(\\sqrt{n":[29],"\\log":[30,149],"n})}$.":[31],"Whether":[32],"polynomial":[39],"remains":[41],"a":[42,120,131,135],"well-known":[43],"open":[44],"question":[45],"area":[48],"of":[49,80,110,116,175,182],"algorithmic":[50],"graph":[51],"theory.":[52],"paper":[55],"we":[56,138],"present":[57],"an":[58,108],"algorithm":[59,79,118,159],"solves":[61],"$2^{\\mathcal{O}(n^{1/3}":[69],"\\log^{2}":[70],"n)}$.":[71],"This":[72,155],"is":[73,119,128,156],"first":[75,158],"improvement":[76],"upon":[77],"general":[86],"case,":[87],"i.e.,":[88],"without":[89],"putting":[90],"any":[91],"further":[92],"restrictions":[93],"on":[94],"instance":[96,109],"graph.":[97],"addition":[99],"to":[100,107,178],"standard":[101],"branchings":[102],"reducing":[104],"2-Sat,":[111],"crucial":[113],"building":[114],"block":[115],"our":[117,176],"combinatorial":[121],"observation":[122],"about":[123],"3-colorable":[124],"graphs,":[126],"which":[127,162],"proven":[129],"using":[130],"probabilistic":[132],"argument.":[133],"As":[134],"side":[136],"result,":[137],"show":[139],"$2^{\\mathcal{O}(":[147],"(n":[148],"n)^{2/3})}$":[150],"diameter-3":[153,169],"graphs.":[154,170],"works":[163],"all":[168],"also":[172],"discuss":[173],"generalizations":[174],"results":[177],"weighted":[180],"variant":[181],"3-Coloring.":[183]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-25T09:21:30.201066","created_date":"2025-10-10T00:00:00"}