{"id":"https://openalex.org/W4416905854","doi":"https://doi.org/10.4230/lipics.wg.2026.31","title":"On the Relation Between Treewidth, Tree-Independence Number, and Tree-Chromatic Number of Graphs","display_name":"On the Relation Between Treewidth, Tree-Independence Number, and Tree-Chromatic Number of Graphs","publication_year":2025,"publication_date":"2025-04-28","ids":{"openalex":"https://openalex.org/W4416905854","doi":"https://doi.org/10.4230/lipics.wg.2026.31"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2504.19751","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2504.19751","pdf_url":"https://arxiv.org/pdf/2504.19751","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,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2504.19751","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5143674734","display_name":"Alex Koutsoutis","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Koutsoutis, Alex","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049267281","display_name":"Kilian Krause","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Krause, Kilian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138832812","display_name":"C Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Chun-Hung","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5143734734","display_name":"Mirza Redzic","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Redzic, Mirza","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063296115","display_name":"Torsten Ueckerdt","orcid":"https://orcid.org/0000-0002-0645-9715"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ueckerdt, Torsten","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057847156","display_name":"Jan Goedgebeur","orcid":"https://orcid.org/0000-0001-8984-2463"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Goedgebeur, Jan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5143690880","display_name":"Pawe\u0142 Rz\u0105\u017cewski","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rz\u0105\u017cewski, Pawe\u0142","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":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.8970999717712402,"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":0.8970999717712402,"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":0.030899999663233757,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.012799999676644802,"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/tree-decomposition","display_name":"Tree decomposition","score":0.6284000277519226},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.5770999789237976},{"id":"https://openalex.org/keywords/tree-depth","display_name":"Tree-depth","score":0.4880000054836273},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.43709999322891235},{"id":"https://openalex.org/keywords/complement-graph","display_name":"Complement graph","score":0.39089998602867126},{"id":"https://openalex.org/keywords/block-graph","display_name":"Block graph","score":0.3894999921321869},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.3398999869823456},{"id":"https://openalex.org/keywords/k-ary-tree","display_name":"K-ary tree","score":0.33070001006126404}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8090000152587891},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7689999938011169},{"id":"https://openalex.org/C70501317","wikidata":"https://www.wikidata.org/wiki/Q462095","display_name":"Tree decomposition","level":5,"score":0.6284000277519226},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.5770999789237976},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.572700023651123},{"id":"https://openalex.org/C69284658","wikidata":"https://www.wikidata.org/wiki/Q7837500","display_name":"Tree-depth","level":5,"score":0.4880000054836273},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.43709999322891235},{"id":"https://openalex.org/C168291704","wikidata":"https://www.wikidata.org/wiki/Q902252","display_name":"Complement graph","level":5,"score":0.39089998602867126},{"id":"https://openalex.org/C43413943","wikidata":"https://www.wikidata.org/wiki/Q4927193","display_name":"Block graph","level":5,"score":0.3894999921321869},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.3398999869823456},{"id":"https://openalex.org/C100560664","wikidata":"https://www.wikidata.org/wiki/Q3608019","display_name":"K-ary tree","level":4,"score":0.33070001006126404},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.32899999618530273},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.32420000433921814},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.31690001487731934},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.2872999906539917},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.27480000257492065},{"id":"https://openalex.org/C5737132","wikidata":"https://www.wikidata.org/wiki/Q1101814","display_name":"Clique-width","level":5,"score":0.26750001311302185},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.26510000228881836},{"id":"https://openalex.org/C2984853995","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independence number","level":3,"score":0.25699999928474426},{"id":"https://openalex.org/C198414033","wikidata":"https://www.wikidata.org/wiki/Q5155607","display_name":"Comparability graph","level":5,"score":0.251800000667572},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":5,"locations":[{"id":"pmh:oai:arXiv.org:2504.19751","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2504.19751","pdf_url":"https://arxiv.org/pdf/2504.19751","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,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:EVASTAR-Karlsruhe.de:1000195632","is_oa":true,"landing_page_url":"https://publikationen.bibliothek.kit.edu/1000195632","pdf_url":"https://publikationen.bibliothek.kit.edu/1000195632/185971178","source":{"id":"https://openalex.org/S4306401992","display_name":"Repository KITopen (Karlsruhe Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102335020","host_organization_name":"Karlsruhe Institute of Technology","host_organization_lineage":["https://openalex.org/I102335020"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1868-8969","raw_type":"doc-type:conferenceObject"},{"id":"doi:10.48550/arxiv.2504.19751","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2504.19751","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,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.4230/lipics.wg.2026.31","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.wg.2026.31","pdf_url":null,"source":{"id":"https://openalex.org/S4393917817","display_name":"Leibniz international proceedings in informatics","issn_l":"1868-8969","issn":["1868-8969"],"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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"ConferencePaper"},{"id":"doi:10.5445/ir/1000195632","is_oa":true,"landing_page_url":"https://doi.org/10.5445/ir/1000195632","pdf_url":null,"source":{"id":"https://openalex.org/S7407052948","display_name":"KITopen","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102335020","host_organization_name":"Karlsruhe Institute of Technology","host_organization_lineage":["https://openalex.org/I102335020"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2504.19751","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2504.19751","pdf_url":"https://arxiv.org/pdf/2504.19751","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,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7982103229","display_name":"Strukturelle Komplexit\u00e4tstheorie f\u00fcr Big Data  Von Klassifikationstheoremen bis Algorithm Engineering","funder_award_id":"462679611","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8652285958","display_name":"ProduktStruktur von Graphen","funder_award_id":"532213793","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416905854.pdf","grobid_xml":"https://content.openalex.org/works/W4416905854.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,103],"investigate":[1],"two":[2],"recently":[3],"introduced":[4],"graph":[5,29,127,164],"parameters,":[6],"both":[7],"of":[8,13,17,27,35,41,45,73,77],"which":[9],"measure":[10,59],"the":[11,14,23,32,48,54,60,65,140],"complexity":[12],"tree":[15,43,75],"decompositions":[16],"a":[18,28,39,71,105,112,126],"given":[19],"graph.":[20],"Recall":[21],"that":[22,94,130,153],"treewidth":[24],"${\\rm":[25,51,57,95,131,154],"tw}(G)$":[26],"$G$":[30,91,128],"measures":[31],"largest":[33,61,66],"number":[34,50,56],"vertices":[36],"required":[37,69],"in":[38,70,111],"bag":[40,72],"every":[42,74,116,163],"decomposition":[44,76],"$G$.":[46,78,165],"Similarly,":[47],"tree-independence":[49],"tree\\textnormal{-}}\u03b1(G)$":[52],"and":[53,82],"tree-chromatic":[55],"tree\\textnormal{-}}\u03c7(G)$":[58,161],"independence":[62],"number,":[63,68],"respectively":[64],"chromatic":[67],"Recently,":[79],"Dallard,":[80],"Milani\u010d,":[81],"\u0160torgel":[83],"asked":[84],"(JCTB,":[85],"2024)":[86],"whether":[87],"for":[88,108,115,162],"all":[89],"graphs":[90],"it":[92],"holds":[93],"tw}(G)+1":[96,155],"\\leq":[97,156],"{\\rm":[98,101,134,157,160],"tree\\textnormal{-}}\u03b1(G)":[99,135],"\\cdot":[100,136,159],"tree\\textnormal{-}}\u03c7(G)$.":[102],"provide":[104],"negative":[106],"answer":[107],"this":[109,145],"question":[110],"strong":[113],"form:":[114],"function":[117],"$f\\colon":[118],"{\\mathbb":[119,122],"N}":[120],"\\rightarrow":[121],"N}$,":[123],"there":[124],"exists":[125],"such":[129],"tw}(G)":[132],"&gt;":[133],"f({\\rm":[137],"tree\\textnormal{-}}\u03c7(G))$.":[138],"On":[139],"other":[141],"hand,":[142],"we":[143],"complement":[144],"result":[146],"with":[147],"an":[148],"upper":[149],"bound,":[150],"by":[151],"showing":[152],"tree\\textnormal{-}}\u03b1(G)^2":[158]},"counts_by_year":[],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}
