{"id":"https://openalex.org/W2101850362","doi":"https://doi.org/10.1007/s00373-012-1199-2","title":"On Minimum Saturated Matrices","display_name":"On Minimum Saturated Matrices","publication_year":2012,"publication_date":"2012-06-18","ids":{"openalex":"https://openalex.org/W2101850362","doi":"https://doi.org/10.1007/s00373-012-1199-2","mag":"2101850362"},"language":"en","primary_location":{"id":"doi:10.1007/s00373-012-1199-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00373-012-1199-2","pdf_url":null,"source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048565272","display_name":"Andrzej Dudek","orcid":"https://orcid.org/0000-0002-6410-5413"},"institutions":[{"id":"https://openalex.org/I141649380","display_name":"Western Michigan University","ror":"https://ror.org/04j198w64","country_code":"US","type":"education","lineage":["https://openalex.org/I141649380"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Andrzej Dudek","raw_affiliation_strings":["Department of Mathematics, Western Michigan University, Kalamazoo, MI, 49008, USA","Department of Mathematics, Western Michigan University, Kalamazoo, USA 49008#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Western Michigan University, Kalamazoo, MI, 49008, USA","institution_ids":["https://openalex.org/I141649380"]},{"raw_affiliation_string":"Department of Mathematics, Western Michigan University, Kalamazoo, USA 49008#TAB#","institution_ids":["https://openalex.org/I141649380"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080095759","display_name":"Oleg Pikhurko","orcid":"https://orcid.org/0000-0002-9657-4011"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]},{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Oleg Pikhurko","raw_affiliation_strings":["Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213, USA","Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, USA 15213 and Mathematics Institute, University of Warwick, Coventry, UK CV4 7AL#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, USA 15213 and Mathematics Institute, University of Warwick, Coventry, UK CV4 7AL#TAB#","institution_ids":["https://openalex.org/I39555362","https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084708925","display_name":"Andrew Thomason","orcid":"https://orcid.org/0000-0002-1805-4221"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Andrew Thomason","raw_affiliation_strings":["Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, CB3 0WB, UK","Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, UK CB3 0WB#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, CB3 0WB, UK","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, UK CB3 0WB#TAB#","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5048565272"],"corresponding_institution_ids":["https://openalex.org/I141649380"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":0.433,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.58559177,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"29","issue":"5","first_page":"1269","last_page":"1286"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9998000264167786,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9984999895095825,"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":0.9984999895095825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8762243390083313},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7632077932357788},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5774574279785156},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.5601899027824402},{"id":"https://openalex.org/keywords/permutation-matrix","display_name":"Permutation matrix","score":0.5436825156211853},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4946455657482147},{"id":"https://openalex.org/keywords/row-and-column-spaces","display_name":"Row and column spaces","score":0.4661160111427307},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.4461126923561096},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4314749538898468},{"id":"https://openalex.org/keywords/row","display_name":"Row","score":0.3656499981880188},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34006643295288086},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11277088522911072},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.0839042067527771},{"id":"https://openalex.org/keywords/circulant-matrix","display_name":"Circulant matrix","score":0.0573573112487793}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8762243390083313},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7632077932357788},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5774574279785156},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.5601899027824402},{"id":"https://openalex.org/C84140500","wikidata":"https://www.wikidata.org/wiki/Q851512","display_name":"Permutation matrix","level":3,"score":0.5436825156211853},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4946455657482147},{"id":"https://openalex.org/C104140500","wikidata":"https://www.wikidata.org/wiki/Q2088159","display_name":"Row and column spaces","level":3,"score":0.4661160111427307},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.4461126923561096},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4314749538898468},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.3656499981880188},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34006643295288086},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11277088522911072},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0839042067527771},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.0573573112487793},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00373-012-1199-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00373-012-1199-2","pdf_url":null,"source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W97263645","https://openalex.org/W1268512041","https://openalex.org/W1502643917","https://openalex.org/W1510730180","https://openalex.org/W1531592115","https://openalex.org/W1971361630","https://openalex.org/W1990490082","https://openalex.org/W1998090738","https://openalex.org/W2004751842","https://openalex.org/W2016740219","https://openalex.org/W2020913456","https://openalex.org/W2021769154","https://openalex.org/W2029657939","https://openalex.org/W2051905988","https://openalex.org/W2053774816","https://openalex.org/W2062920840","https://openalex.org/W2114935567","https://openalex.org/W2161815929","https://openalex.org/W2498848698","https://openalex.org/W2913796054","https://openalex.org/W4212812385","https://openalex.org/W4229606576","https://openalex.org/W4255941684"],"related_works":["https://openalex.org/W2313440505","https://openalex.org/W3123744736","https://openalex.org/W1505848319","https://openalex.org/W2137691148","https://openalex.org/W2905020035","https://openalex.org/W4281399881","https://openalex.org/W3166006430","https://openalex.org/W1974627484","https://openalex.org/W2152668278","https://openalex.org/W2019569581"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}