{"id":"https://openalex.org/W4400467622","doi":"https://doi.org/10.1137/23m1591773","title":"Product Structure Extension of the Alon\u2013Seymour\u2013Thomas Theorem","display_name":"Product Structure Extension of the Alon\u2013Seymour\u2013Thomas Theorem","publication_year":2024,"publication_date":"2024-07-09","ids":{"openalex":"https://openalex.org/W4400467622","doi":"https://doi.org/10.1137/23m1591773"},"language":"en","primary_location":{"id":"doi:10.1137/23m1591773","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1591773","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":true,"oa_status":"green","oa_url":"https://dipot.ulb.ac.be/dspace/bitstream/2013/376701/3/2212.08739v4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090988242","display_name":"Marc Distel","orcid":"https://orcid.org/0000-0003-0122-1430"},"institutions":[{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Marc Distel","raw_affiliation_strings":["School of Mathematics, Monash University, Melbourne, Victoria, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Monash University, Melbourne, Victoria, Australia","institution_ids":["https://openalex.org/I56590836"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000058655","display_name":"Vida Dujmovi\u0107","orcid":"https://orcid.org/0000-0001-7250-0600"},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"education","lineage":["https://openalex.org/I153718931"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Vida Dujmovi\u0107","raw_affiliation_strings":["School of Computer Science and Electrical Engineering, University of Ottawa, Ottawa, ON, K1N 6N5, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Electrical Engineering, University of Ottawa, Ottawa, ON, K1N 6N5, Canada","institution_ids":["https://openalex.org/I153718931"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108527295","display_name":"David Eppstein","orcid":null},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]},{"id":"https://openalex.org/I4210140791","display_name":"Irvine University","ror":"https://ror.org/04ysmca02","country_code":"US","type":"education","lineage":["https://openalex.org/I4210140791"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David Eppstein","raw_affiliation_strings":["Computer Science Department, University of California, Irvine, Irvine, CA 92697-3425 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, University of California, Irvine, Irvine, CA 92697-3425 USA","institution_ids":["https://openalex.org/I204250578","https://openalex.org/I4210140791"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086019567","display_name":"Robert Hickingbotham","orcid":"https://orcid.org/0009-0007-1817-8295"},"institutions":[{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Robert Hickingbotham","raw_affiliation_strings":["School of Mathematics, Monash University, Melbourne, Victoria, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Monash University, Melbourne, Victoria, Australia","institution_ids":["https://openalex.org/I56590836"]}]},{"author_position":"middle","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"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Gwena\u00ebl Joret","raw_affiliation_strings":["D\u00e9partement d\u2019Informatique, Universit\u00e9 libre de Bruxelles, Brussels, 1050, Belgium"],"raw_orcid":"https://orcid.org/0000-0002-7157-6694","affiliations":[{"raw_affiliation_string":"D\u00e9partement d\u2019Informatique, Universit\u00e9 libre de Bruxelles, Brussels, 1050, Belgium","institution_ids":["https://openalex.org/I132053463"]}]},{"author_position":"middle","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"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Piotr Micek","raw_affiliation_strings":["Department of Theoretical Computer Science, Jagiellonian University, Krak\u00f3w, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Theoretical Computer Science, Jagiellonian University, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045902784","display_name":"Pat Morin","orcid":"https://orcid.org/0000-0003-0471-4118"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Pat Morin","raw_affiliation_strings":["School of Computer Science, Carleton University, Ottawa, Ontario, K1S 5B6, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, Carleton University, Ottawa, Ontario, K1S 5B6, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067222052","display_name":"Micha\u0142 T. Seweryn","orcid":"https://orcid.org/0000-0002-9090-3435"},"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"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Micha\u0142 T. Seweryn","raw_affiliation_strings":["D\u00e9partement d\u2019Informatique, Universit\u00e9 libre de Bruxelles, Brussels, 1050, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement d\u2019Informatique, Universit\u00e9 libre de Bruxelles, Brussels, 1050, Belgium","institution_ids":["https://openalex.org/I132053463"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066302647","display_name":"David R. Wood","orcid":"https://orcid.org/0000-0001-8866-3041"},"institutions":[{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"David R. Wood","raw_affiliation_strings":["School of Mathematics, Monash University, Melbourne, Victoria, Australia"],"raw_orcid":"https://orcid.org/0000-0001-8866-3041","affiliations":[{"raw_affiliation_string":"School of Mathematics, Monash University, Melbourne, Victoria, Australia","institution_ids":["https://openalex.org/I56590836"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":7,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0289,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.77889994,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"38","issue":"3","first_page":"2095","last_page":"2107"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T11476","display_name":"Graph theory and applications","score":0.998199999332428,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9980999827384949,"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/mathematics","display_name":"Mathematics","score":0.8652635812759399},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.7362730503082275},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6788437962532043},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.6018680334091187},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48657000064849854},{"id":"https://openalex.org/keywords/structured-program-theorem","display_name":"Structured program theorem","score":0.4295027554035187},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08599671721458435},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07454702258110046}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8652635812759399},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.7362730503082275},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6788437962532043},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.6018680334091187},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48657000064849854},{"id":"https://openalex.org/C180375552","wikidata":"https://www.wikidata.org/wiki/Q2635326","display_name":"Structured program theorem","level":2,"score":0.4295027554035187},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08599671721458435},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07454702258110046},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/23m1591773","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1591773","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"},{"id":"pmh:oai:dipot.ulb.ac.be:2013/376701","is_oa":true,"landing_page_url":"http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/376701","pdf_url":"https://dipot.ulb.ac.be/dspace/bitstream/2013/376701/3/2212.08739v4.pdf","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":"SIAM journal on discrete mathematics, 38 (3","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:ruj.uj.edu.pl:item/570085","is_oa":true,"landing_page_url":"https://ruj.uj.edu.pl/handle/item/570085","pdf_url":null,"source":{"id":"https://openalex.org/S4306401249","display_name":"Jagiellonian University Repository (Jagiellonian University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126596746","host_organization_name":"Jagiellonian University","host_organization_lineage":["https://openalex.org/I126596746"],"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":"info:eu-repo/semantics/article"},{"id":"pmh:oai:escholarship.org:ark:/13030/qt2z3410hc","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/2z3410hc","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"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":"SIAM Journal on Discrete Mathematics, vol 38, iss 3","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:dipot.ulb.ac.be:2013/376701","is_oa":true,"landing_page_url":"http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/376701","pdf_url":"https://dipot.ulb.ac.be/dspace/bitstream/2013/376701/3/2212.08739v4.pdf","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":"SIAM journal on discrete mathematics, 38 (3","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1691068924","display_name":null,"funder_award_id":"UMO-2018/31/G/ST1/03718","funder_id":"https://openalex.org/F4320322511","funder_display_name":"Narodowe Centrum Nauki"},{"id":"https://openalex.org/G4740345469","display_name":null,"funder_award_id":"CCF-2212129","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7210885136","display_name":"Collaborative Research: AF: Medium: Algorithms for Geometric Graphs","funder_award_id":"2212129","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320315885","display_name":"Australian Government","ror":"https://ror.org/0314h5y94"},{"id":"https://openalex.org/F4320321390","display_name":"Fonds De La Recherche Scientifique - FNRS","ror":"https://ror.org/03q83t159"},{"id":"https://openalex.org/F4320322511","display_name":"Narodowe Centrum Nauki","ror":"https://ror.org/03ha2q922"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"},{"id":"https://openalex.org/F4320336370","display_name":"Ontario Ministry of Research and Innovation","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400467622.pdf"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W621909926","https://openalex.org/W1982180670","https://openalex.org/W2035409201","https://openalex.org/W2038643780","https://openalex.org/W2051655695","https://openalex.org/W2057826895","https://openalex.org/W2073558110","https://openalex.org/W2087083200","https://openalex.org/W2128660769","https://openalex.org/W2145062394","https://openalex.org/W2170136611","https://openalex.org/W2345501529","https://openalex.org/W2519651985","https://openalex.org/W2938191358","https://openalex.org/W2963730044","https://openalex.org/W3007271564","https://openalex.org/W3014452398","https://openalex.org/W3103394879","https://openalex.org/W3106391534","https://openalex.org/W3188704289","https://openalex.org/W3216235219","https://openalex.org/W4319589071","https://openalex.org/W4385308338","https://openalex.org/W4389451502"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2075768550","https://openalex.org/W3022218857","https://openalex.org/W2369178846","https://openalex.org/W2370289839","https://openalex.org/W2082716031","https://openalex.org/W2933494595","https://openalex.org/W2950435018","https://openalex.org/W2624065397","https://openalex.org/W2525865568"],"abstract_inverted_index":{"Alon,":[0],"Seymour,":[1],"and":[2,30,84],"Thomas":[3],"[J.":[4],"Amer.":[5],"Math.":[6],"Soc.,":[7],"3":[8],"(1990),":[9],"pp.":[10],"801-808]":[11],"proved":[12],"that":[13,49,89,119],"every":[14,50],"n-vertex":[15],"graph":[16,52,58,73],"excluding":[17],"Kt":[18],"as":[19],"a":[20,54,71],"minor":[21],"has":[22],"treewidth":[23,60,91,121],"less":[24],"than":[25],"t3/2":[26],"\\\\surdn.":[27],"Illingworth,":[28,82],"Scott,":[29,83],"Wood":[31,85],"[Product":[32],"Structure":[33],"of":[34,56,74,81,101,107,114,141],"Graphs":[35],"with":[36,59,139],"an":[37,78,105],"Excluded":[38],"Minor,":[39],"preprint,":[40],"arXiv:2104.06627,":[41],"2022]":[42],"recently":[43],"refined":[44],"this":[45,134],"result":[46,135],"by":[47,70],"showing":[48],"such":[51],"is":[53,67,129],"subgraph":[55],"some":[57],"t":[61],"-":[62],"2,":[63,127],"where":[64],"each":[65],"vertex":[66],"blown":[68],"up":[69],"complete":[72],"order":[75,102,142],"\\\\scrO(\\\\surdtn).":[76],"Solving":[77],"open":[79],"problem":[80],"[2022],":[86],"we":[87,117],"prove":[88],"the":[90,108,112,120],"bound":[92],"can":[93,122],"be":[94,123],"reduced":[95,125],"to":[96,126],"4":[97],"while":[98],"keeping":[99],"blowups":[100,140],"\\\\scrOt(\\\\surdn).":[103],"As":[104],"extension":[106],"Lipton-Tarjan":[109],"theorem,":[110],"in":[111],"case":[113],"planar":[115],"graphs,":[116,138],"show":[118],"further":[124],"which":[128],"best":[130],"possible.":[131],"We":[132],"generalize":[133],"for":[136],"K3,t-minor-free":[137],"\\\\scrO(t\\\\surdn).":[143],"This":[144],"setting":[145],"includes":[146],"graphs":[147],"embeddable":[148],"on":[149],"any":[150],"fixed":[151],"surface.":[152]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
