{"id":"https://openalex.org/W2171757450","doi":"https://doi.org/10.37236/386","title":"Recognizing Graph Theoretic Properties with Polynomial Ideals","display_name":"Recognizing Graph Theoretic Properties with Polynomial Ideals","publication_year":2010,"publication_date":"2010-08-16","ids":{"openalex":"https://openalex.org/W2171757450","doi":"https://doi.org/10.37236/386","mag":"2171757450"},"language":"en","primary_location":{"id":"doi:10.37236/386","is_oa":true,"landing_page_url":"https://doi.org/10.37236/386","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r114/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r114/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055755657","display_name":"Jes\u00fas A. De Loera","orcid":"https://orcid.org/0000-0002-9556-1112"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]},{"id":"https://openalex.org/I73544541","display_name":"Mathematical Sciences Research Institute","ror":"https://ror.org/05hs5r386","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I73544541"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jes\u00fas A. De Loera","raw_affiliation_strings":["Mathematical Sciences Research Institute, Berkeley, CA 94120","University of California, Davis, Davis, CA 95616"],"affiliations":[{"raw_affiliation_string":"Mathematical Sciences Research Institute, Berkeley, CA 94120","institution_ids":["https://openalex.org/I73544541"]},{"raw_affiliation_string":"University of California, Davis, Davis, CA 95616","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039959148","display_name":"Christopher J. Hillar","orcid":"https://orcid.org/0000-0001-8575-2663"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]},{"id":"https://openalex.org/I73544541","display_name":"Mathematical Sciences Research Institute","ror":"https://ror.org/05hs5r386","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I73544541"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christopher J. Hillar","raw_affiliation_strings":["University of California, Davis, Davis, CA 95616","Mathematical Sciences Research Institute, Berkeley, CA 94120"],"affiliations":[{"raw_affiliation_string":"University of California, Davis, Davis, CA 95616","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"Mathematical Sciences Research Institute, Berkeley, CA 94120","institution_ids":["https://openalex.org/I73544541"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086599845","display_name":"Peter N. Malkin","orcid":null},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]},{"id":"https://openalex.org/I73544541","display_name":"Mathematical Sciences Research Institute","ror":"https://ror.org/05hs5r386","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I73544541"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peter N. Malkin","raw_affiliation_strings":["University of California, Davis, Davis, CA 95616","Mathematical Sciences Research Institute, Berkeley, CA 94120"],"affiliations":[{"raw_affiliation_string":"University of California, Davis, Davis, CA 95616","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"Mathematical Sciences Research Institute, Berkeley, CA 94120","institution_ids":["https://openalex.org/I73544541"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101855842","display_name":"Mohamed Omar","orcid":"https://orcid.org/0000-0003-2133-0781"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]},{"id":"https://openalex.org/I73544541","display_name":"Mathematical Sciences Research Institute","ror":"https://ror.org/05hs5r386","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I73544541"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mohamed Omar","raw_affiliation_strings":["University of California, Davis, Davis, CA 95616","Mathematical Sciences Research Institute, Berkeley, CA 94120"],"affiliations":[{"raw_affiliation_string":"University of California, Davis, Davis, CA 95616","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"Mathematical Sciences Research Institute, Berkeley, CA 94120","institution_ids":["https://openalex.org/I73544541"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5055755657"],"corresponding_institution_ids":["https://openalex.org/I73544541","https://openalex.org/I84218800"],"apc_list":null,"apc_paid":null,"fwci":4.1869,"has_fulltext":true,"cited_by_count":22,"citation_normalized_percentile":{"value":0.94520891,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"17","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9983000159263611,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9957000017166138,"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":0.8198568820953369},{"id":"https://openalex.org/keywords/system-of-polynomial-equations","display_name":"System of polynomial equations","score":0.6259229779243469},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5324721336364746},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5006136894226074},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.49860215187072754},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49064627289772034},{"id":"https://openalex.org/keywords/stable-polynomial","display_name":"Stable polynomial","score":0.43486088514328003},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.42366480827331543},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.405620276927948},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38190099596977234},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2550744414329529},{"id":"https://openalex.org/keywords/alternating-polynomial","display_name":"Alternating polynomial","score":0.25085848569869995}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8198568820953369},{"id":"https://openalex.org/C105335568","wikidata":"https://www.wikidata.org/wiki/Q7663735","display_name":"System of polynomial equations","level":3,"score":0.6259229779243469},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5324721336364746},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5006136894226074},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.49860215187072754},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49064627289772034},{"id":"https://openalex.org/C45025165","wikidata":"https://www.wikidata.org/wiki/Q13424738","display_name":"Stable polynomial","level":5,"score":0.43486088514328003},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.42366480827331543},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.405620276927948},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38190099596977234},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2550744414329529},{"id":"https://openalex.org/C170412648","wikidata":"https://www.wikidata.org/wiki/Q4736415","display_name":"Alternating polynomial","level":4,"score":0.25085848569869995},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/386","is_oa":true,"landing_page_url":"https://doi.org/10.37236/386","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r114/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:scholarship.claremont.edu:hmc_fac_pub-1811","is_oa":false,"landing_page_url":"https://scholarship.claremont.edu/hmc_fac_pub/806","pdf_url":null,"source":{"id":"https://openalex.org/S4377196412","display_name":"Scholarship - Claremont (Claremont Colleges)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I872248612","host_organization_name":"Claremont Colleges","host_organization_lineage":["https://openalex.org/I872248612"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"All HMC Faculty Publications and Research","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.176.3421","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.176.3421","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_17/PDF/v17i1r114.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.182.3443","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.182.3443","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.msri.org/people/members/chillar/files/ejc.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/386","is_oa":true,"landing_page_url":"https://doi.org/10.37236/386","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r114/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2171757450.pdf","grobid_xml":"https://content.openalex.org/works/W2171757450.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W145923007","https://openalex.org/W600377564","https://openalex.org/W1487891397","https://openalex.org/W1490896784","https://openalex.org/W1500642430","https://openalex.org/W1505369303","https://openalex.org/W1506764403","https://openalex.org/W1529743226","https://openalex.org/W1583871653","https://openalex.org/W1603558703","https://openalex.org/W1828856524","https://openalex.org/W1967184028","https://openalex.org/W1976596704","https://openalex.org/W1977561651","https://openalex.org/W1989517190","https://openalex.org/W1990618633","https://openalex.org/W1992202796","https://openalex.org/W1995621089","https://openalex.org/W1997672673","https://openalex.org/W1999647319","https://openalex.org/W2030996579","https://openalex.org/W2033864528","https://openalex.org/W2037002007","https://openalex.org/W2038079294","https://openalex.org/W2045652876","https://openalex.org/W2069288321","https://openalex.org/W2072414205","https://openalex.org/W2073039945","https://openalex.org/W2079705627","https://openalex.org/W2081659888","https://openalex.org/W2099652582","https://openalex.org/W2106138233","https://openalex.org/W2106264302","https://openalex.org/W2128687423","https://openalex.org/W2132489129","https://openalex.org/W2133602590","https://openalex.org/W2153918277","https://openalex.org/W2167831266","https://openalex.org/W2171471009","https://openalex.org/W2280936352","https://openalex.org/W2319466955","https://openalex.org/W2485530965","https://openalex.org/W2911280162","https://openalex.org/W2970485886","https://openalex.org/W3090330333","https://openalex.org/W3105023213","https://openalex.org/W4210508986","https://openalex.org/W4231656836","https://openalex.org/W4285719527","https://openalex.org/W4301403801","https://openalex.org/W6604641075","https://openalex.org/W6815079546"],"related_works":["https://openalex.org/W2963637113","https://openalex.org/W1543706171","https://openalex.org/W2084988136","https://openalex.org/W148891984","https://openalex.org/W1964170686","https://openalex.org/W2391577669","https://openalex.org/W1998109337","https://openalex.org/W3185830269","https://openalex.org/W2355559409","https://openalex.org/W2124841895"],"abstract_inverted_index":{"Many":[0],"hard":[1],"combinatorial":[2,29],"problems":[3],"can":[4,48],"be":[5,49],"modeled":[6],"by":[7],"a":[8],"system":[9],"of":[10,24,35,45,59],"polynomial":[11,18,37,46],"equations.":[12],"N.":[13],"Alon":[14],"coined":[15],"the":[16,22,33,36,42],"term":[17],"method":[19,38],"to":[20,51],"describe":[21],"use":[23],"nonlinear":[25],"polynomials":[26],"when":[27],"solving":[28],"problems.":[30],"We":[31],"continue":[32],"exploration":[34],"and":[39,56,65,80],"show":[40],"how":[41],"algorithmic":[43],"theory":[44],"ideals":[47],"used":[50],"detect":[52],"$k$-colorability,":[53],"unique":[54],"Hamiltonicity,":[55],"automorphism":[57],"rigidity":[58],"graphs.":[60],"Our":[61],"techniques":[62],"are":[63],"diverse":[64],"involve":[66],"Nullstellensatz":[67],"certificates,":[68],"linear":[69],"algebra":[70],"over":[71],"finite":[72],"fields,":[73],"Gr\u00f6bner":[74],"bases,":[75],"toric":[76],"algebra,":[77],"convex":[78],"programming,":[79],"real":[81],"algebraic":[82],"geometry.":[83]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}