{"id":"https://openalex.org/W7223249286","doi":"https://doi.org/10.48550/arxiv.2610.28865","title":"Tree-independence number VIII. 3PC-free graphs have logarithmic tree-independence number","display_name":"Tree-independence number VIII. 3PC-free graphs have logarithmic tree-independence number","publication_year":2026,"publication_date":"2026-10-20","ids":{"openalex":"https://openalex.org/W7223249286","doi":"https://doi.org/10.48550/arxiv.2610.28865"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.28865","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28865","pdf_url":"https://arxiv.org/pdf/2610.28865","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/2610.28865","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028345325","display_name":"Maria Chudnovsky","orcid":"https://orcid.org/0000-0002-8920-4944","observed_orcids":["https://orcid.org/0000-0002-8920-4944"]},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chudnovsky, Maria","raw_affiliation_strings":["Princeton University , Princeton , NJ , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University , Princeton , NJ , USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5099136871","display_name":"Julien Codsi","orcid":"https://orcid.org/0009-0003-2881-1825","observed_orcids":["https://orcid.org/0009-0003-2881-1825"]},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Codsi, Julien","raw_affiliation_strings":["Department of Computer Science , University of California Santa Barbara , Santa Barbara , CA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science , University of California Santa Barbara , Santa Barbara , CA , USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5122083825","display_name":"Ajaykrishnan E S","orcid":"https://orcid.org/0009-0001-4080-3647","observed_orcids":["https://orcid.org/0009-0001-4080-3647"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S, Ajaykrishnan E","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038531405","display_name":"Daniel Lokshtanov","orcid":"https://orcid.org/0000-0002-3166-9212","observed_orcids":["https://orcid.org/0000-0002-3166-9212"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lokshtanov, Daniel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5125387430","display_name":"Ilya Maier","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Maier, Ilya","raw_affiliation_strings":["Princeton University , Princeton , NJ , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University , Princeton , NJ , USA","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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":0.9976000189781189,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.0012000000569969416,"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":0.000699999975040555,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/logarithmic-bounds","display_name":"logarithmic bounds","score":0.6069999933242798},{"id":"https://openalex.org/keywords/induced-subgraphs","display_name":"induced subgraphs","score":0.7089999914169312},{"id":"https://openalex.org/keywords/extremal-graph-theory","display_name":"extremal graph theory","score":0.7129999995231628}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.795199990272522},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7591999769210815},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6157000064849854},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5620999932289124},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5230000019073486},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48420000076293945},{"id":"https://openalex.org/C59824394","wikidata":"https://www.wikidata.org/wiki/Q5141281","display_name":"Cograph","level":5,"score":0.3774999976158142},{"id":"https://openalex.org/C43413943","wikidata":"https://www.wikidata.org/wiki/Q4927193","display_name":"Block graph","level":5,"score":0.37549999356269836},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.35339999198913574},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.31459999084472656},{"id":"https://openalex.org/C128115575","wikidata":"https://www.wikidata.org/wiki/Q5597083","display_name":"Graph factorization","level":5,"score":0.3003999888896942},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.296999990940094},{"id":"https://openalex.org/C67810366","wikidata":"https://www.wikidata.org/wiki/Q835942","display_name":"Interval graph","level":5,"score":0.27149999141693115},{"id":"https://openalex.org/C147792647","wikidata":"https://www.wikidata.org/wiki/Q5282847","display_name":"Distance-hereditary graph","level":5,"score":0.2662999927997589},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.28865","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28865","pdf_url":"https://arxiv.org/pdf/2610.28865","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":"doi:10.48550/arxiv.2610.28865","doi":"https://doi.org/10.48550/arxiv.2610.28865","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.28865","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.28865","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28865","pdf_url":"https://arxiv.org/pdf/2610.28865","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":[{"id":"https://openalex.org/G5115329756","display_name":"Collaborative Research: AF:Medium: Structure and Quasi-Polynomial Time Algorithms","funder_award_id":"2505100","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5974638285","display_name":"Forbidding Induced Subgraphs: Decompositions, Coloring and Algorithms","funder_award_id":"2348219","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7474739737","display_name":"Collaborative Research: AF:Medium: Structure and Quasi-Polynomial Time Algorithms","funder_award_id":"2505099","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7886378241","display_name":null,"funder_award_id":"CCF-2505099","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309292","display_name":"Princeton University","ror":"https://ror.org/00hx57361"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223249286.pdf","grobid_xml":"https://content.openalex.org/works/W7223249286.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7160325603"],"related_works":["https://openalex.org/W4414056851","https://openalex.org/W4399912319","https://openalex.org/W7148786914","https://openalex.org/W3197941146","https://openalex.org/W4414631968","https://openalex.org/W3043442232","https://openalex.org/W4414696166","https://openalex.org/W7160428726","https://openalex.org/W97909189","https://openalex.org/W1964543450"],"abstract_inverted_index":{"A":[0,28],"three-path-configuration":[1],"is":[2,19,30,38,51],"a":[3,39],"graph":[4,29],"consisting":[5],"of":[6,14,17,23,36],"three":[7],"pairwise":[8],"internally":[9],"vertex-disjoint":[10],"paths,":[11],"the":[12],"union":[13],"every":[15],"two":[16],"which":[18,50],"an":[20],"induced":[21,34],"cycle":[22],"length":[24],"at":[25],"least":[26],"four.":[27],"3PC-free":[31,44],"if":[32],"no":[33],"subgraph":[35],"it":[37],"three-path-configuration.":[40],"We":[41],"show":[42],"that":[43],"graphs":[45],"have":[46],"logarithmic":[47],"tree-independence":[48],"number,":[49],"asymptotically":[52],"best":[53],"possible.":[54]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-23T00:00:00"}