{"id":"https://openalex.org/W1523869344","doi":"https://doi.org/10.1007/978-3-642-18469-7_26","title":"Dot Product Representations of Planar Graphs","display_name":"Dot Product Representations of Planar Graphs","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1523869344","doi":"https://doi.org/10.1007/978-3-642-18469-7_26","mag":"1523869344"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-18469-7_26","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-642-18469-7_26","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-642-18469-7_26.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-642-18469-7_26.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019911064","display_name":"Ross J. Kang","orcid":"https://orcid.org/0000-0002-4219-593X"},"institutions":[{"id":"https://openalex.org/I190082696","display_name":"Durham University","ror":"https://ror.org/01v29qb04","country_code":"GB","type":"education","lineage":["https://openalex.org/I190082696"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Ross J. Kang","raw_affiliation_strings":["Durham University, UK","Durham University"],"affiliations":[{"raw_affiliation_string":"Durham University, UK","institution_ids":["https://openalex.org/I190082696"]},{"raw_affiliation_string":"Durham University","institution_ids":["https://openalex.org/I190082696"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077475001","display_name":"Tobias M\u00fcller","orcid":"https://orcid.org/0000-0002-5964-7867"},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Tobias M\u00fcller","raw_affiliation_strings":["Centrum Wiskunde & Informatica#TAB#"],"affiliations":[{"raw_affiliation_string":"Centrum Wiskunde & Informatica#TAB#","institution_ids":["https://openalex.org/I1341640284"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019911064"],"corresponding_institution_ids":["https://openalex.org/I190082696"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.7728,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.72616712,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"287","last_page":"292"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9988999962806702,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9919999837875366,"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/dot-product","display_name":"Dot product","score":0.7214891910552979},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6739048361778259},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.6370327472686768},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5846470594406128},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.49389058351516724},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.46165478229522705},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38585004210472107},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38334596157073975},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37927937507629395},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07477676868438721},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.06085506081581116}],"concepts":[{"id":"https://openalex.org/C32900221","wikidata":"https://www.wikidata.org/wiki/Q181365","display_name":"Dot product","level":2,"score":0.7214891910552979},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6739048361778259},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.6370327472686768},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5846470594406128},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.49389058351516724},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.46165478229522705},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38585004210472107},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38334596157073975},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37927937507629395},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07477676868438721},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.06085506081581116}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/978-3-642-18469-7_26","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-642-18469-7_26","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-642-18469-7_26.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:cwi.nl:18584","is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/18584","pdf_url":"https://ir.cwi.nl/pub/18584/18584.pdf","source":{"id":"https://openalex.org/S7407055335","display_name":"Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Electronic Journal of Combinatorics vol. 18 no. 1","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:cwi:oai:cwi.nl:16773","is_oa":false,"landing_page_url":"https://ir.cwi.nl/pub/16773","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferencepaper"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.372.6859","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.372.6859","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/ojs/index.php/eljc/article/viewFile/v18i1p216/pdf/","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.874.4025","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.874.4025","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.staff.science.uu.nl/%7Emuell001/Papers/dotproductPlanarGD.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.883.4484","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.883.4484","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.staff.science.uu.nl/%7Emuell001/Papers/dotproductPlanar.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1007/978-3-642-18469-7_26","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-642-18469-7_26","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-642-18469-7_26.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1934935867","display_name":null,"funder_award_id":"Engineering and Physical Sciences R","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G283985778","display_name":null,"funder_award_id":"EP/G066604/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G629491556","display_name":null,"funder_award_id":"(NWO)","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G6318140058","display_name":"Approximation and mixing times in the ferromagnetic Potts model","funder_award_id":"EP/G066604/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1523869344.pdf","grobid_xml":"https://content.openalex.org/works/W1523869344.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1521990134","https://openalex.org/W1570340896","https://openalex.org/W1968034334","https://openalex.org/W1971048994","https://openalex.org/W1978219425","https://openalex.org/W2001505356","https://openalex.org/W2008671796","https://openalex.org/W2019029270","https://openalex.org/W2065805017","https://openalex.org/W2078289947","https://openalex.org/W2123750718","https://openalex.org/W4256581173"],"related_works":["https://openalex.org/W4206327962","https://openalex.org/W2010009304","https://openalex.org/W1996851061","https://openalex.org/W3021694725","https://openalex.org/W3216105633","https://openalex.org/W1701875187","https://openalex.org/W2990956612","https://openalex.org/W1606013690","https://openalex.org/W4293743430","https://openalex.org/W3006156235"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}