{"id":"https://openalex.org/W4414577375","doi":"https://doi.org/10.1007/s00493-025-00177-9","title":"Trees and near-linear stable sets","display_name":"Trees and near-linear stable sets","publication_year":2025,"publication_date":"2025-09-25","ids":{"openalex":"https://openalex.org/W4414577375","doi":"https://doi.org/10.1007/s00493-025-00177-9"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-025-00177-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-025-00177-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00177-9.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00177-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100642009","display_name":"Tung Nguyen","orcid":"https://orcid.org/0000-0003-4232-0566"},"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":"Tung Nguyen","raw_affiliation_strings":["Princeton University, Princeton, NJ, 08544, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University, Princeton, NJ, 08544, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045091550","display_name":"Alex Scott","orcid":"https://orcid.org/0000-0003-4489-5988"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Alex Scott","raw_affiliation_strings":["University of Oxford, Oxford, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Oxford, Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031948088","display_name":"Paul Seymour","orcid":"https://orcid.org/0000-0003-0067-4534"},"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":"Paul Seymour","raw_affiliation_strings":["Princeton University, Princeton, NJ, 08544, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University, Princeton, NJ, 08544, USA","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5045091550"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.25833611,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"45","issue":"5","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":0.958899974822998,"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":0.958899974822998,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9445000290870667,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9294999837875366,"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/conjecture","display_name":"Conjecture","score":0.660099983215332},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5705999732017517},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5552999973297119},{"id":"https://openalex.org/keywords/induced-subgraph","display_name":"Induced subgraph","score":0.48190000653266907},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.4700999855995178},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.43160000443458557},{"id":"https://openalex.org/keywords/independent-set","display_name":"Independent set","score":0.3898000121116638},{"id":"https://openalex.org/keywords/split-graph","display_name":"Split graph","score":0.3871999979019165}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9225999712944031},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7882999777793884},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.660099983215332},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5705999732017517},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5552999973297119},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49320000410079956},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.48190000653266907},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.4700999855995178},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.43160000443458557},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.3898000121116638},{"id":"https://openalex.org/C8554925","wikidata":"https://www.wikidata.org/wiki/Q3893853","display_name":"Split graph","level":5,"score":0.3871999979019165},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.3278000056743622},{"id":"https://openalex.org/C189239283","wikidata":"https://www.wikidata.org/wiki/Q17101022","display_name":"Clique graph","level":5,"score":0.3248000144958496},{"id":"https://openalex.org/C128115575","wikidata":"https://www.wikidata.org/wiki/Q5597083","display_name":"Graph factorization","level":5,"score":0.3156000077724457},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.29789999127388},{"id":"https://openalex.org/C36038622","wikidata":"https://www.wikidata.org/wiki/Q5428703","display_name":"Factor-critical graph","level":5,"score":0.2872999906539917},{"id":"https://openalex.org/C191241153","wikidata":"https://www.wikidata.org/wiki/Q6027240","display_name":"Induced subgraph isomorphism problem","level":5,"score":0.2669000029563904},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C150591576","wikidata":"https://www.wikidata.org/wiki/Q739925","display_name":"Family of sets","level":3,"score":0.2583000063896179},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C147792647","wikidata":"https://www.wikidata.org/wiki/Q5282847","display_name":"Distance-hereditary graph","level":5,"score":0.2565000057220459}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00493-025-00177-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-025-00177-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00177-9.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00493-025-00177-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-025-00177-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00177-9.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G1940970491","display_name":null,"funder_award_id":"EP/X013642/","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2146822515","display_name":null,"funder_award_id":"DMS-2154169","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3448263929","display_name":"DMS-EPSRC INDUCED SUBGRAPHS AND GRAPH STRUCTURE","funder_award_id":"EP/X013642/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4764071259","display_name":null,"funder_award_id":"FA9550-22-1-0234","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5745604493","display_name":"DMS-EPRSC: Induced Subgraphs and Graph Structure","funder_award_id":"2154169","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5809100787","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6447070560","display_name":null,"funder_award_id":"DMS-2154169","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G7461889428","display_name":null,"funder_award_id":"FA9550-22-1-0234","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/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414577375.pdf"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W2029442750","https://openalex.org/W2051336598","https://openalex.org/W2053858915","https://openalex.org/W2094108224","https://openalex.org/W2098242693","https://openalex.org/W2331072996","https://openalex.org/W2962935610","https://openalex.org/W2978867875","https://openalex.org/W3080973359","https://openalex.org/W3186740737","https://openalex.org/W4229970255","https://openalex.org/W4254094289","https://openalex.org/W4392591899","https://openalex.org/W4399973656"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"When":[1],"H":[2,20,72,90],"is":[3,73,91,95],"a":[4,27,46,75,82,92,96,103,111],"forest,":[5,76],"the":[6,116,127],"Gy\u00e1rf\u00e1s-Sumner":[7,117],"conjecture":[8],"implies":[9],"that":[10,40,88,107],"every":[11,41],"graph":[12,43],"G":[13,44],"with":[14,22],"no":[15],"induced":[16],"subgraph":[17],"isomorphic":[18],"to":[19,126],"and":[21],"bounded":[23],"clique":[24],"number":[25],"has":[26,45],"stable":[28,47,83,97],"set":[29,48,98],"of":[30,49,99,115,123],"linear":[31,100],"size.":[32,101],"We":[33],"cannot":[34],"prove":[35,39,87],"that,":[36],"but":[37],"we":[38,86,105,120],"such":[42,81],"size":[50],"$$|G|^{1-o(1)}$$":[51],"<mml:math":[52],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[53],"<mml:msup>":[54],"<mml:mrow>":[55,60],"<mml:mo>|</mml:mo>":[56,58],"<mml:mi>G</mml:mi>":[57],"</mml:mrow>":[59,67],"<mml:mn>1</mml:mn>":[61,65],"<mml:mo>-</mml:mo>":[62],"<mml:mi>o</mml:mi>":[63],"<mml:mo>(</mml:mo>":[64],"<mml:mo>)</mml:mo>":[66],"</mml:msup>":[68],"</mml:math>":[69],".":[70],"If":[71],"not":[74,79],"there":[77,94],"need":[78],"be":[80],"set.":[84],"Second,":[85],"when":[89],"\u201cmultibroom\u201d,":[93],"As":[102],"consequence,":[104],"deduce":[106],"all":[108],"multibrooms":[109],"satisfy":[110],"\u201cfractional":[112],"colouring\u201d":[113],"version":[114],"conjecture.":[118],"Finally,":[119],"discuss":[121],"extensions":[122],"our":[124],"results":[125],"multicolour":[128],"setting.":[129]},"counts_by_year":[],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}
