{"id":"https://openalex.org/W3129935410","doi":"https://doi.org/10.37236/10274","title":"Improved Bounds for Weak Coloring Numbers","display_name":"Improved Bounds for Weak Coloring Numbers","publication_year":2022,"publication_date":"2022-03-25","ids":{"openalex":"https://openalex.org/W3129935410","doi":"https://doi.org/10.37236/10274","mag":"3129935410"},"language":"en","primary_location":{"id":"doi:10.37236/10274","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10274","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p60/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p60/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038947183","display_name":"Gwena\u00ebl Joret","orcid":"https://orcid.org/0000-0002-7157-6694"},"institutions":[{"id":"https://openalex.org/I132053463","display_name":"Universit\u00e9 Libre de Bruxelles","ror":"https://ror.org/01r9htc13","country_code":"BE","type":"education","lineage":["https://openalex.org/I132053463"]},{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["BE","PL"],"is_corresponding":true,"raw_author_name":"Gwena\u00ebl Joret","raw_affiliation_strings":["Computer Science Department Universit\u00e9 libre de Bruxelles Brussels, Belgium","Theoretical Computer Science Department Jagiellonian University Krak\u00f3w, Poland"],"affiliations":[{"raw_affiliation_string":"Computer Science Department Universit\u00e9 libre de Bruxelles Brussels, Belgium","institution_ids":["https://openalex.org/I132053463"]},{"raw_affiliation_string":"Theoretical Computer Science Department Jagiellonian University Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107964690","display_name":"Piotr Micek","orcid":"https://orcid.org/0000-0001-9796-5375"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]},{"id":"https://openalex.org/I132053463","display_name":"Universit\u00e9 Libre de Bruxelles","ror":"https://ror.org/01r9htc13","country_code":"BE","type":"education","lineage":["https://openalex.org/I132053463"]}],"countries":["BE","PL"],"is_corresponding":false,"raw_author_name":"Piotr Micek","raw_affiliation_strings":["Computer Science Department Universit\u00e9 libre de Bruxelles Brussels, Belgium","Theoretical Computer Science Department Jagiellonian University Krak\u00f3w, Poland"],"affiliations":[{"raw_affiliation_string":"Computer Science Department Universit\u00e9 libre de Bruxelles Brussels, Belgium","institution_ids":["https://openalex.org/I132053463"]},{"raw_affiliation_string":"Theoretical Computer Science Department Jagiellonian University Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038947183"],"corresponding_institution_ids":["https://openalex.org/I126596746","https://openalex.org/I132053463"],"apc_list":null,"apc_paid":null,"fwci":0.6012,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.68157058,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"29","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":1.0,"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":1.0,"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":0.9993000030517578,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9976000189781189,"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":0.8432446718215942},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7291249632835388},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.6646329760551453},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.6430791616439819},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.6257443428039551},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.5698694586753845},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5377919673919678},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5151726007461548},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5145298838615417},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48779112100601196},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.42059704661369324},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.23196151852607727},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10854434967041016},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.10640904307365417}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8432446718215942},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7291249632835388},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.6646329760551453},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.6430791616439819},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.6257443428039551},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.5698694586753845},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5377919673919678},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5151726007461548},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5145298838615417},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48779112100601196},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.42059704661369324},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.23196151852607727},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10854434967041016},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.10640904307365417},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/10274","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10274","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p60/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2102.10061","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2102.10061","pdf_url":"https://arxiv.org/pdf/2102.10061","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},{"id":"pmh:oai:ruj.uj.edu.pl:item/308006","is_oa":true,"landing_page_url":"https://ruj.uj.edu.pl/xmlui/handle/item/308006","pdf_url":"http://ruj.uj.edu.pl/bitstreams/89bb23d3-4d69-4cf7-a8ac-0e86d4c9d73c/download","source":{"id":"https://openalex.org/S4306400316","display_name":"Homo Politicus (Academy of Humanities and Economics in Lodz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"artyku\u0142 w czasopi\u015bmie"},{"id":"pmh:oai:dipot.ulb.ac.be:2013/336950","is_oa":true,"landing_page_url":"http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/336950","pdf_url":null,"source":{"id":"https://openalex.org/S4306401063","display_name":"D\u00e9p\u00f4t institutionnel de l'Universit\u00e9 libre de Bruxelles (Universit\u00e9 Libre de Bruxelles)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I132053463","host_organization_name":"Universit\u00e9 Libre de Bruxelles","host_organization_lineage":["https://openalex.org/I132053463"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The electronic journal of combinatorics, 29 (1","raw_type":"info:ulb-repo/semantics/openurl/article"}],"best_oa_location":{"id":"doi:10.37236/10274","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10274","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p60/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321390","display_name":"Fonds De La Recherche Scientifique - FNRS","ror":"https://ror.org/03q83t159"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3129935410.pdf","grobid_xml":"https://content.openalex.org/works/W3129935410.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W1580700984","https://openalex.org/W1815738779","https://openalex.org/W1973674396","https://openalex.org/W1999552793","https://openalex.org/W2105469400","https://openalex.org/W2143305437","https://openalex.org/W2149573503","https://openalex.org/W2177898499","https://openalex.org/W2296234613","https://openalex.org/W2561061762","https://openalex.org/W2565975294","https://openalex.org/W2611328153","https://openalex.org/W2755112968","https://openalex.org/W2765807423","https://openalex.org/W2898841741","https://openalex.org/W2938191358","https://openalex.org/W2953085759","https://openalex.org/W2953295957","https://openalex.org/W2958527737","https://openalex.org/W2962961215","https://openalex.org/W2963893440","https://openalex.org/W2964417322","https://openalex.org/W2966179270","https://openalex.org/W2978811879","https://openalex.org/W2998163837","https://openalex.org/W3001329909","https://openalex.org/W3081344375","https://openalex.org/W3094053427","https://openalex.org/W3103394879","https://openalex.org/W3110610715","https://openalex.org/W3125642972","https://openalex.org/W3172663538","https://openalex.org/W3175737004","https://openalex.org/W3194359700","https://openalex.org/W4288083072","https://openalex.org/W4292424416","https://openalex.org/W4293575831","https://openalex.org/W4302318575","https://openalex.org/W6743144113","https://openalex.org/W6755210204","https://openalex.org/W6779724142"],"related_works":["https://openalex.org/W3216545571","https://openalex.org/W4312183469","https://openalex.org/W4285484079","https://openalex.org/W4301463689","https://openalex.org/W2605313623","https://openalex.org/W124636724","https://openalex.org/W2952055179","https://openalex.org/W4302786124","https://openalex.org/W1557579971","https://openalex.org/W3198523758"],"abstract_inverted_index":{"Weak":[0],"coloring":[1,33,60,85],"numbers":[2,34],"generalize":[3],"the":[4,19,56,77,81],"notion":[5],"of":[6,8,21,62,87,101],"degeneracy":[7],"a":[9,63,73,98],"graph.":[10],"They":[11],"were":[12],"introduced":[13],"by":[14],"Kierstead":[15],"&":[16],"Yang":[17],"in":[18,39],"context":[20],"games":[22],"on":[23,80],"graphs.":[24,106],"Recently,":[25],"several":[26],"connections":[27],"have":[28],"been":[29],"uncovered":[30],"between":[31],"weak":[32,59,84],"and":[35,43,95],"various":[36],"parameters":[37],"studied":[38],"graph":[40,64],"minor":[41],"theory":[42],"its":[44],"generalizations.":[45],"In":[46],"this":[47],"note,":[48],"we":[49,75,96],"show":[50],"that":[51],"for":[52,104],"every":[53],"fixed":[54],"$k\\geq1$,":[55],"maximum":[57,82],"$r$-th":[58,83],"number":[61,86],"with":[65],"simple":[66],"treewidth":[67],"$k$":[68],"is":[69],"$\\Theta(r^{k-1}\\log":[70],"r)$.":[71],"As":[72],"corollary,":[74],"improve":[76],"lower":[78],"bound":[79,100],"planar":[88],"graphs":[89],"from":[90],"$\\Omega(r^2)$":[91],"to":[92],"$\\Omega(r^2\\log":[93],"r)$,":[94],"obtain":[97],"tight":[99],"$\\Theta(r\\log":[102],"r)$":[103],"outerplanar":[105]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}