{"id":"https://openalex.org/W2032055415","doi":"https://doi.org/10.1145/1824801.1824802","title":"Computing Tutte Polynomials","display_name":"Computing Tutte Polynomials","publication_year":2010,"publication_date":"2010-09-01","ids":{"openalex":"https://openalex.org/W2032055415","doi":"https://doi.org/10.1145/1824801.1824802","mag":"2032055415"},"language":"en","primary_location":{"id":"doi:10.1145/1824801.1824802","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1824801.1824802","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","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/A5026736818","display_name":"Gary Haggard","orcid":null},"institutions":[{"id":"https://openalex.org/I131221577","display_name":"Bucknell University","ror":"https://ror.org/00fc1qt65","country_code":"US","type":"education","lineage":["https://openalex.org/I131221577"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gary Haggard","raw_affiliation_strings":["Bucknell University","(Bucknell University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bucknell University","institution_ids":["https://openalex.org/I131221577"]},{"raw_affiliation_string":"(Bucknell University","institution_ids":["https://openalex.org/I131221577"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008538442","display_name":"David J. Pearce","orcid":"https://orcid.org/0000-0003-4535-9677"},"institutions":[{"id":"https://openalex.org/I41156924","display_name":"Victoria University of Wellington","ror":"https://ror.org/0040r6f76","country_code":"NZ","type":"education","lineage":["https://openalex.org/I41156924"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"David J. Pearce","raw_affiliation_strings":["Victoria University of Wellington, NZ","Victoria University of Wellington, NZ#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Victoria University of Wellington, NZ","institution_ids":["https://openalex.org/I41156924"]},{"raw_affiliation_string":"Victoria University of Wellington, NZ#TAB#","institution_ids":["https://openalex.org/I41156924"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071503218","display_name":"Gordon Royle","orcid":"https://orcid.org/0000-0003-2669-4437"},"institutions":[{"id":"https://openalex.org/I177877127","display_name":"The University of Western Australia","ror":"https://ror.org/047272k79","country_code":"AU","type":"education","lineage":["https://openalex.org/I177877127"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Gordon Royle","raw_affiliation_strings":["University of Western, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Western, Australia","institution_ids":["https://openalex.org/I177877127"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.8374,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.96622671,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"37","issue":"3","first_page":"1","last_page":"17"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9986000061035156,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9986000061035156,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/tutte-polynomial","display_name":"Tutte polynomial","score":0.9791156649589539},{"id":"https://openalex.org/keywords/chromatic-polynomial","display_name":"Chromatic polynomial","score":0.8996993899345398},{"id":"https://openalex.org/keywords/potts-model","display_name":"Potts model","score":0.6890196204185486},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6295326352119446},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.611470103263855},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5437191724777222},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.5237386226654053},{"id":"https://openalex.org/keywords/bracket-polynomial","display_name":"Bracket polynomial","score":0.5006496906280518},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.38919463753700256},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.3409627079963684},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.30882787704467773},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.2635161280632019},{"id":"https://openalex.org/keywords/alternating-polynomial","display_name":"Alternating polynomial","score":0.2427440881729126},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.21615079045295715}],"concepts":[{"id":"https://openalex.org/C14447369","wikidata":"https://www.wikidata.org/wiki/Q7857002","display_name":"Tutte polynomial","level":5,"score":0.9791156649589539},{"id":"https://openalex.org/C126385604","wikidata":"https://www.wikidata.org/wiki/Q1087609","display_name":"Chromatic polynomial","level":3,"score":0.8996993899345398},{"id":"https://openalex.org/C98925819","wikidata":"https://www.wikidata.org/wiki/Q7235385","display_name":"Potts model","level":3,"score":0.6890196204185486},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6295326352119446},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.611470103263855},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5437191724777222},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.5237386226654053},{"id":"https://openalex.org/C52007518","wikidata":"https://www.wikidata.org/wiki/Q4953698","display_name":"Bracket polynomial","level":5,"score":0.5006496906280518},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.38919463753700256},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.3409627079963684},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.30882787704467773},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.2635161280632019},{"id":"https://openalex.org/C170412648","wikidata":"https://www.wikidata.org/wiki/Q4736415","display_name":"Alternating polynomial","level":4,"score":0.2427440881729126},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.21615079045295715},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.0},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/1824801.1824802","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1824801.1824802","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/c44f63af-21b5-40bb-bde3-0e8138d4fbe8","is_oa":false,"landing_page_url":"https://research-repository.uwa.edu.au/en/publications/c44f63af-21b5-40bb-bde3-0e8138d4fbe8","pdf_url":null,"source":{"id":"https://openalex.org/S4306402523","display_name":"UWA Profiles and Research Repository (University of Western Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177877127","host_organization_name":"The University of Western Australia","host_organization_lineage":["https://openalex.org/I177877127"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Haggard , G , Pearce , D J & Royle , G 2010 , ' Computing Tutte Polynomials ' , ACM Transactions on Mathematical Software , vol. 37 , pp. - . https://doi.org/10.1145/1824801.1824802","raw_type":"article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.3551","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.3551","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.newton.cam.ac.uk/preprints/NI09024.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.306.7911","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.306.7911","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://homepages.mcs.vuw.ac.nz/~djp/files/TOMS10.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6833894952","display_name":null,"funder_award_id":"737730","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W188858573","https://openalex.org/W195048868","https://openalex.org/W1490787220","https://openalex.org/W1492445835","https://openalex.org/W1503513951","https://openalex.org/W1531965102","https://openalex.org/W1534309112","https://openalex.org/W1966233265","https://openalex.org/W1971911032","https://openalex.org/W1994556169","https://openalex.org/W2004308928","https://openalex.org/W2010255818","https://openalex.org/W2011473996","https://openalex.org/W2039758366","https://openalex.org/W2039763834","https://openalex.org/W2055585984","https://openalex.org/W2069731308","https://openalex.org/W2084667559","https://openalex.org/W2096833188","https://openalex.org/W2101387049","https://openalex.org/W2118382442","https://openalex.org/W2142148165","https://openalex.org/W2148360835","https://openalex.org/W2156361153","https://openalex.org/W2314361409","https://openalex.org/W2496833595","https://openalex.org/W2561675875","https://openalex.org/W2964638337","https://openalex.org/W2964650941","https://openalex.org/W3021394452","https://openalex.org/W3098202978","https://openalex.org/W3194776842","https://openalex.org/W4206109200"],"related_works":["https://openalex.org/W3124123742","https://openalex.org/W2121298904","https://openalex.org/W1968430479","https://openalex.org/W4280592647","https://openalex.org/W4302506957","https://openalex.org/W2527934888","https://openalex.org/W3099881882","https://openalex.org/W2167608572","https://openalex.org/W2032055415","https://openalex.org/W1648918722"],"abstract_inverted_index":{"The":[0],"Tutte":[1,80,120],"polynomial":[2,21,37,43,46,81],"of":[3,12,24,58,82,86,96,110,127,136,141,146],"a":[4,19,83,97,134,147],"graph,":[5],"also":[6],"known":[7],"as":[8,40,47,55,61],"the":[9,13,41,56,79,94,103,108,125,128,139,142],"partition":[10],"function":[11],"q":[14],"-state":[15],"Potts":[16],"model":[17],"is":[18,115],"2-variable":[20],"graph":[22,85],"invariant":[23],"considerable":[25],"importance":[26],"in":[27,102],"both":[28],"combinatorics":[29],"and":[30,44,50,122],"statistical":[31],"physics.":[32],"It":[33],"contains":[34],"several":[35],"other":[36],"invariants,":[38],"such":[39,54],"chromatic":[42],"flow":[45,144],"partial":[48],"evaluations,":[49],"various":[51],"numerical":[52],"invariants":[53],"number":[57],"spanning":[59],"trees":[60],"complete":[62],"evaluations.":[63],"However":[64],"despite":[65],"its":[66],"ubiquity,":[67],"there":[68],"are":[69],"no":[70],"widely":[71],"available":[72],"effective":[73],"computational":[74],"tools":[75],"able":[76],"to":[77,106,117,133],"compute":[78,118],"general":[84],"reasonable":[87],"size.":[88],"In":[89],"this":[90],"article":[91],"we":[92,123],"describe":[93],"implementation":[95],"program":[98,129],"that":[99],"exploits":[100],"isomorphisms":[101],"computation":[104],"tree":[105],"extend":[107],"range":[109],"graphs":[111],"for":[112],"which":[113],"it":[114],"feasible":[116],"their":[119],"polynomials,":[121],"demonstrate":[124],"utility":[126],"by":[130],"finding":[131],"counterexamples":[132],"conjecture":[135],"Welsh":[137],"on":[138],"location":[140],"real":[143],"roots":[145],"graph.":[148]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}