{"id":"https://openalex.org/W1862096312","doi":"https://doi.org/10.25596/jalc-2008-045","title":"On Representable Graphs","display_name":"On Representable Graphs","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1862096312","doi":"https://doi.org/10.25596/jalc-2008-045","mag":"1862096312"},"language":"en","primary_location":{"id":"pmh:oai:strathprints.strath.ac.uk:49898","is_oa":false,"landing_page_url":"https://strathprints.strath.ac.uk/view/author/780334.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4306402226","display_name":"Strathprints: The University of Strathclyde institutional repository (University of Strathclyde)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I181647926","host_organization_name":"University of Strathclyde","host_organization_lineage":["https://openalex.org/I181647926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.25596/jalc-2008-045","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024451009","display_name":"Sergey Kitaev","orcid":"https://orcid.org/0000-0003-3324-1647"},"institutions":[{"id":"https://openalex.org/I123185442","display_name":"Reykjav\u00edk University","ror":"https://ror.org/05d2kyx68","country_code":"IS","type":"education","lineage":["https://openalex.org/I123185442"]}],"countries":["IS"],"is_corresponding":true,"raw_author_name":"Kitaev, Sergey","raw_affiliation_strings":["Reykjav\u00edk University, Reykjav\u00ed Iceland#TAB#"],"affiliations":[{"raw_affiliation_string":"Reykjav\u00edk University, Reykjav\u00ed Iceland#TAB#","institution_ids":["https://openalex.org/I123185442"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089643426","display_name":"A. V. Pyatkin","orcid":"https://orcid.org/0000-0001-5355-411X"},"institutions":[{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Pyatkin, Artem","raw_affiliation_strings":["Sobolev Institute of Mathematics, Novosibirsk, Russia#TAB#"],"affiliations":[{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, Russia#TAB#","institution_ids":["https://openalex.org/I4210096862"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024451009"],"corresponding_institution_ids":["https://openalex.org/I123185442"],"apc_list":null,"apc_paid":null,"fwci":2.058,"has_fulltext":true,"cited_by_count":33,"citation_normalized_percentile":{"value":0.86025965,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"13","issue":"1","first_page":"45","last_page":"54"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9991999864578247,"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":0.9991999864578247,"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/T11567","display_name":"semigroups and automata theory","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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/alphabet","display_name":"Alphabet","score":0.7320379018783569},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6827921271324158},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5765959620475769},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5716155171394348},{"id":"https://openalex.org/keywords/existential-quantification","display_name":"Existential quantification","score":0.4994008541107178},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4399242699146271},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.054361939430236816}],"concepts":[{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.7320379018783569},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6827921271324158},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5765959620475769},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5716155171394348},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.4994008541107178},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4399242699146271},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.054361939430236816},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:strathprints.strath.ac.uk:49898","is_oa":false,"landing_page_url":"https://strathprints.strath.ac.uk/view/author/780334.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4306402226","display_name":"Strathprints: The University of Strathclyde institutional repository (University of Strathclyde)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I181647926","host_organization_name":"University of Strathclyde","host_organization_lineage":["https://openalex.org/I181647926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.121.1579","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.121.1579","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ru.is/papers/sergey_repgr.pdf","raw_type":"text"},{"id":"doi:10.25596/jalc-2008-045","is_oa":true,"landing_page_url":"https://doi.org/10.25596/jalc-2008-045","pdf_url":null,"source":{"id":"https://openalex.org/S7407052944","display_name":"Justus-Liebig-Universit\u00e4t Gie\u00dfen","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"mag:1862096312","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/journals/jalc/jalc13.html#KitaevP08","pdf_url":null,"source":{"id":"https://openalex.org/S62907800","display_name":"Journal of automata, languages and combinatorics","issn_l":"1430-189X","issn":["1430-189X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313929","host_organization_name":"University of Giessen","host_organization_lineage":["https://openalex.org/P4310313929"],"host_organization_lineage_names":["University of Giessen"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Journal of automata, languages and combinatorics","raw_type":null}],"best_oa_location":{"id":"doi:10.25596/jalc-2008-045","is_oa":true,"landing_page_url":"https://doi.org/10.25596/jalc-2008-045","pdf_url":null,"source":{"id":"https://openalex.org/S7407052944","display_name":"Justus-Liebig-Universit\u00e4t Gie\u00dfen","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W3242420","https://openalex.org/W2132524082"],"related_works":["https://openalex.org/W2092388212","https://openalex.org/W2269342346","https://openalex.org/W2911323838","https://openalex.org/W1595742662","https://openalex.org/W1767557960","https://openalex.org/W1614901210","https://openalex.org/W2071001022","https://openalex.org/W1921317569","https://openalex.org/W1597416101","https://openalex.org/W2086223441","https://openalex.org/W2614598353","https://openalex.org/W2154534416","https://openalex.org/W2222082663","https://openalex.org/W3100632572","https://openalex.org/W2952798981","https://openalex.org/W2964241391","https://openalex.org/W2218676601","https://openalex.org/W166539567","https://openalex.org/W2760409917","https://openalex.org/W1776116583"],"abstract_inverted_index":{"A":[0],"graph":[1,58],"$G":[2],"=":[3],"(V,E)$":[4],"is":[5,37,51,59,66],"representable":[6,60],"if":[7,26,29,61,64],"there":[8],"exists":[9],"a":[10,57],"word":[11],"$W$":[12,25,36,42],"over":[13],"the":[14],"alphabet":[15],"$V$":[16],"such":[17],"that":[18,56],"letters":[19],"$x$":[20],"and":[21,27,62,90],"$y$":[22],"alternate":[23],"in":[24,47,77],"only":[28,63],"$(x,y)\\in":[30],"E$":[31],"for":[32,68],"each":[33],"$x\\not=y$.":[34],"If":[35],"$k$-uniform":[38],"(each":[39],"letter":[40],"of":[41,72,83],"occurs":[43],"exactly":[44],"$k$":[45],"times":[46],"it)":[48],"then":[49],"$G$":[50],"called":[52],"$k$-representable.":[53],"We":[54],"prove":[55],"it":[65],"$k$-representable":[67],"some":[69],"$k$.":[70],"Examples":[71],"non-representable":[73],"graphs":[74,84],"are":[75,85,95],"found":[76],"this":[78],"paper.":[79],"Some":[80],"Wide":[81],"classes":[82],"proven":[86],"to":[87],"be":[88],"2-":[89],"3-representable.":[91],"Several":[92],"open":[93],"problems":[94],"stated.":[96]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}