{"id":"https://openalex.org/W2766037965","doi":"https://doi.org/10.1080/10586458.2018.1437851","title":"Lower Bounds on the Number of Realizations of Rigid Graphs","display_name":"Lower Bounds on the Number of Realizations of Rigid Graphs","publication_year":2018,"publication_date":"2018-03-27","ids":{"openalex":"https://openalex.org/W2766037965","doi":"https://doi.org/10.1080/10586458.2018.1437851","mag":"2766037965","pmid":"https://pubmed.ncbi.nlm.nih.gov/32655833"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2018.1437851","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.2018.1437851","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/10586458.2018.1437851?needAccess=true","source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.tandfonline.com/doi/pdf/10.1080/10586458.2018.1437851?needAccess=true","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Georg Grasegger","orcid":"https://orcid.org/0000-0001-7421-8115"},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"government","lineage":["https://openalex.org/I138211613"]},{"id":"https://openalex.org/I4210158379","display_name":"Johann Radon Institute for Computational and Applied Mathematics","ror":"https://ror.org/05a94k872","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Georg Grasegger","raw_affiliation_strings":["Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, Austria"],"raw_orcid":"https://orcid.org/0000-0001-7421-8115","affiliations":[{"raw_affiliation_string":"Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, Austria","institution_ids":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Christoph Koutschan","orcid":"https://orcid.org/0000-0003-1135-3082"},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"government","lineage":["https://openalex.org/I138211613"]},{"id":"https://openalex.org/I4210158379","display_name":"Johann Radon Institute for Computational and Applied Mathematics","ror":"https://ror.org/05a94k872","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Christoph Koutschan","raw_affiliation_strings":["Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, Austria"],"raw_orcid":"https://orcid.org/0000-0003-1135-3082","affiliations":[{"raw_affiliation_string":"Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, Austria","institution_ids":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}]},{"author_position":"last","author":{"id":null,"display_name":"Elias Tsigaridas","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210159731","display_name":"LIP6","ror":"https://ror.org/05krcen59","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210159245","https://openalex.org/I4210159731"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Elias Tsigaridas","raw_affiliation_strings":["Sorbonne Universit\u00e9s, UPMC Univ Paris 06, CNRS, INRIA, Laboratoire d\u2019Informatique de Paris 6 (LIP6), \u00c9quipe PolSys, Paris Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sorbonne Universit\u00e9s, UPMC Univ Paris 06, CNRS, INRIA, Laboratoire d\u2019Informatique de Paris 6 (LIP6), \u00c9quipe PolSys, Paris Cedex, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I39804081","https://openalex.org/I4210159731"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I138211613","https://openalex.org/I4210158379"],"apc_list":null,"apc_paid":null,"fwci":0.1976,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.51853664,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"29","issue":"2","first_page":"125","last_page":"136"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11870","display_name":"Structural Analysis and Optimization","score":0.9664000272750854,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11870","display_name":"Structural Analysis and Optimization","score":0.9664000272750854,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.006800000090152025,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11737","display_name":"Advanced Materials and Mechanics","score":0.005200000014156103,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.550599992275238},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4311999976634979},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4124000072479248},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.3490000069141388},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.33869999647140503},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.3273000121116638}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8064000010490417},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5746999979019165},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.550599992275238},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4311999976634979},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4124000072479248},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41110000014305115},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.3490000069141388},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.33869999647140503},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.3273000121116638},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2912999987602234},{"id":"https://openalex.org/C187407849","wikidata":"https://www.wikidata.org/wiki/Q6889712","display_name":"Modular decomposition","level":5,"score":0.2702000141143799},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.25609999895095825}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/10586458.2018.1437851","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.2018.1437851","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/10586458.2018.1437851?needAccess=true","source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmid:32655833","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/32655833","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental mathematics","raw_type":null},{"id":"pmh:oai:arXiv.org:1710.08237","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.08237","pdf_url":"https://arxiv.org/pdf/1710.08237","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7324120","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7324120","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Exp Math","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1080/10586458.2018.1437851","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.2018.1437851","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/10586458.2018.1437851?needAccess=true","source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1405593087","display_name":null,"funder_award_id":"W1214\u2010N15","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G1558722870","display_name":"Games through the lens of ALgebra and geometry of OPtimization","funder_award_id":"ANR-17-CE40-0009","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G340885496","display_name":null,"funder_award_id":"F5011-N15","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2766037965.pdf"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1948893736","https://openalex.org/W2013407568","https://openalex.org/W2026588045","https://openalex.org/W2030668278","https://openalex.org/W2037009986","https://openalex.org/W2044933794","https://openalex.org/W2046598752","https://openalex.org/W2060706474","https://openalex.org/W2081415437","https://openalex.org/W2093547815","https://openalex.org/W2114049990","https://openalex.org/W2117819179","https://openalex.org/W2139834426","https://openalex.org/W2736265251","https://openalex.org/W2784208434"],"related_works":[],"abstract_inverted_index":{"Computing":[0],"the":[1,25,37,51,67],"number":[2,70,79],"of":[3,5,30,53,71,80],"realizations":[4,73],"a":[6,11,31,62,77],"minimally":[7,22],"rigid":[8,23,56,87],"graph":[9],"is":[10,36,44],"notoriously":[12],"difficult":[13],"problem.":[14],"Toward":[15],"this":[16],"goal,":[17],"for":[18,74],"graphs":[19,57,75,88],"that":[20],"are":[21],"in":[24,89],"plane,":[26],"we":[27,60,93],"take":[28],"advantage":[29],"recently":[32],"published":[33],"algorithm,":[34],"which":[35],"fastest":[38],"available":[39],"method,":[40],"although":[41],"its":[42],"complexity":[43],"still":[45],"exponential.":[46],"Combining":[47],"computational":[48],"results":[49],"with":[50,76],"theory":[52],"constructing":[54],"new":[55,63],"by":[58,98],"gluing,":[59],"give":[61],"lower":[64,96],"bound":[65],"on":[66],"maximal":[68],"possible":[69],"(complex)":[72],"given":[78],"vertices.":[81],"We":[82],"extend":[83],"these":[84],"ideas":[85],"to":[86],"three":[90],"dimensions":[91],"and":[92],"derive":[94],"similar":[95],"bounds,":[97],"exploiting":[99],"data":[100],"from":[101],"extensive":[102],"Gr\u00f6bner":[103],"basis":[104],"computations.":[105]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2017-11-10T00:00:00"}