{"id":"https://openalex.org/W2100223096","doi":"https://doi.org/10.1007/s00453-015-0016-8","title":"Two-Page Book Embeddings of 4-Planar Graphs","display_name":"Two-Page Book Embeddings of 4-Planar Graphs","publication_year":2015,"publication_date":"2015-06-15","ids":{"openalex":"https://openalex.org/W2100223096","doi":"https://doi.org/10.1007/s00453-015-0016-8","mag":"2100223096"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-015-0016-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00453-015-0016-8","pdf_url":null,"source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","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/A5006472576","display_name":"Michael A. Bekos","orcid":"https://orcid.org/0000-0002-3414-7444"},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Michael A. Bekos","raw_affiliation_strings":["Wilhelm-Schickhard-Institut f\u00fcr Informatik, Universit\u00e4t T\u00fcbingen, T\u00fcbingen, Germany"],"affiliations":[{"raw_affiliation_string":"Wilhelm-Schickhard-Institut f\u00fcr Informatik, Universit\u00e4t T\u00fcbingen, T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I8087733"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080178526","display_name":"Martin Gronemann","orcid":"https://orcid.org/0000-0003-2565-090X"},"institutions":[{"id":"https://openalex.org/I180923762","display_name":"University of Cologne","ror":"https://ror.org/00rcxh774","country_code":"DE","type":"education","lineage":["https://openalex.org/I180923762"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Gronemann","raw_affiliation_strings":["Institut f\u00fcr Informatik, Universit\u00e4t zu K\u00f6ln, Cologne, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, Universit\u00e4t zu K\u00f6ln, Cologne, Germany","institution_ids":["https://openalex.org/I180923762"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056184296","display_name":"Chrysanthi N. Raftopoulou","orcid":"https://orcid.org/0000-0001-6457-516X"},"institutions":[{"id":"https://openalex.org/I174458059","display_name":"National Technical University of Athens","ror":"https://ror.org/03cx6bg69","country_code":"GR","type":"education","lineage":["https://openalex.org/I174458059"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Chrysanthi N. Raftopoulou","raw_affiliation_strings":["School of Applied Mathematical and Physical Sciences, NTUA, Athens, Greece","School of Applied Mathematical and Physical Sciences, NTUA, Athens, Greece#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Applied Mathematical and Physical Sciences, NTUA, Athens, Greece","institution_ids":["https://openalex.org/I174458059"]},{"raw_affiliation_string":"School of Applied Mathematical and Physical Sciences, NTUA, Athens, Greece#TAB#","institution_ids":["https://openalex.org/I174458059"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5006472576"],"corresponding_institution_ids":["https://openalex.org/I8087733"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.5465,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.89985128,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"75","issue":"1","first_page":"158","last_page":"185"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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":0.9995999932289124,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9843999743461609,"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/book-embedding","display_name":"Book embedding","score":0.8258041143417358},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.7772640585899353},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6522201895713806},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.6346344351768494},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.5930615663528442},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5907358527183533},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.5297257304191589},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5226839780807495},{"id":"https://openalex.org/keywords/outerplanar-graph","display_name":"Outerplanar graph","score":0.5224422812461853},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.5105355978012085},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.465643048286438},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4572545886039734},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45598769187927246},{"id":"https://openalex.org/keywords/clique-sum","display_name":"Clique-sum","score":0.44854846596717834},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.42112377285957336},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35946911573410034},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3452893793582916},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12740644812583923},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.11398571729660034}],"concepts":[{"id":"https://openalex.org/C180222743","wikidata":"https://www.wikidata.org/wiki/Q4942980","display_name":"Book embedding","level":5,"score":0.8258041143417358},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.7772640585899353},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6522201895713806},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.6346344351768494},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.5930615663528442},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5907358527183533},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.5297257304191589},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5226839780807495},{"id":"https://openalex.org/C125792925","wikidata":"https://www.wikidata.org/wiki/Q3115604","display_name":"Outerplanar graph","level":5,"score":0.5224422812461853},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5105355978012085},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.465643048286438},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4572545886039734},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45598769187927246},{"id":"https://openalex.org/C186942658","wikidata":"https://www.wikidata.org/wiki/Q5134410","display_name":"Clique-sum","level":5,"score":0.44854846596717834},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.42112377285957336},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35946911573410034},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3452893793582916},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12740644812583923},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.11398571729660034},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","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":1,"locations":[{"id":"doi:10.1007/s00453-015-0016-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00453-015-0016-8","pdf_url":null,"source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W151167536","https://openalex.org/W1490863509","https://openalex.org/W1491152805","https://openalex.org/W1966802404","https://openalex.org/W1967125711","https://openalex.org/W1983755786","https://openalex.org/W1998294201","https://openalex.org/W2003073299","https://openalex.org/W2005042684","https://openalex.org/W2032200149","https://openalex.org/W2050065904","https://openalex.org/W2119115989","https://openalex.org/W2143668983","https://openalex.org/W4237169760","https://openalex.org/W4237617962","https://openalex.org/W4288073110"],"related_works":["https://openalex.org/W603403972","https://openalex.org/W3101895193","https://openalex.org/W2133160845","https://openalex.org/W2442922754","https://openalex.org/W2950027724","https://openalex.org/W4298164694","https://openalex.org/W2801149745","https://openalex.org/W1979858320","https://openalex.org/W1483059930","https://openalex.org/W1483552525"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
