{"id":"https://openalex.org/W28463467","doi":"https://doi.org/10.1007/978-0-8176-4904-3_2","title":"An Information-Theoretic Upper Bound on Planar Graphs Using Well-Orderly Maps","display_name":"An Information-Theoretic Upper Bound on Planar Graphs Using Well-Orderly Maps","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W28463467","doi":"https://doi.org/10.1007/978-0-8176-4904-3_2","mag":"28463467"},"language":"en","primary_location":{"id":"doi:10.1007/978-0-8176-4904-3_2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-0-8176-4904-3_2","pdf_url":null,"source":{"id":"https://openalex.org/S4306462921","display_name":"Birkh\u00e4user Boston eBooks","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":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Towards an Information Theory of Complex Networks","raw_type":"book-chapter"},"type":"book-chapter","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/A5107031577","display_name":"Nicolas Bonichon","orcid":"https://orcid.org/0000-0002-7012-6851"},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nicolas Bonichon","raw_affiliation_strings":["LaBRI, University of Bordeaux, 351 Cours de la lib\u00e9ration, 33405, Bordeaux, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LaBRI, University of Bordeaux, 351 Cours de la lib\u00e9ration, 33405, Bordeaux, France","institution_ids":["https://openalex.org/I15057530","https://openalex.org/I4210142254"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013587418","display_name":"Cyril Gavoille","orcid":"https://orcid.org/0000-0003-3671-8607"},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Cyril Gavoille","raw_affiliation_strings":["LaBRI, University of Bordeaux, 351 Cours de la lib\u00e9ration, 33405, Bordeaux, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LaBRI, University of Bordeaux, 351 Cours de la lib\u00e9ration, 33405, Bordeaux, France","institution_ids":["https://openalex.org/I15057530","https://openalex.org/I4210142254"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047477217","display_name":"Nicolas Hanusse","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nicolas Hanusse","raw_affiliation_strings":["LaBRI, CNRS \u2013 University of Bordeaux, 351 Cours de la lib\u00e9ration, 33405, Bordeaux, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LaBRI, CNRS \u2013 University of Bordeaux, 351 Cours de la lib\u00e9ration, 33405, Bordeaux, France","institution_ids":["https://openalex.org/I15057530","https://openalex.org/I1294671590","https://openalex.org/I4210142254"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3727,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58771382,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"17","last_page":"46"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11269","display_name":"Algorithms and Data Compression","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T12029","display_name":"DNA and Biological Computing","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.8370308876037598},{"id":"https://openalex.org/keywords/book-embedding","display_name":"Book embedding","score":0.7266624569892883},{"id":"https://openalex.org/keywords/planar-straight-line-graph","display_name":"Planar straight-line graph","score":0.6658993363380432},{"id":"https://openalex.org/keywords/outerplanar-graph","display_name":"Outerplanar graph","score":0.6233638525009155},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6061890721321106},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5902789831161499},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.5881271958351135},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.5594409704208374},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.5167876482009888},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.46517276763916016},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4643675684928894},{"id":"https://openalex.org/keywords/polyhedral-graph","display_name":"Polyhedral graph","score":0.4434836804866791},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.3514993190765381},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.336406409740448},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.30100017786026},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2269999384880066},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0549299418926239}],"concepts":[{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.8370308876037598},{"id":"https://openalex.org/C180222743","wikidata":"https://www.wikidata.org/wiki/Q4942980","display_name":"Book embedding","level":5,"score":0.7266624569892883},{"id":"https://openalex.org/C131930043","wikidata":"https://www.wikidata.org/wiki/Q7200964","display_name":"Planar straight-line graph","level":5,"score":0.6658993363380432},{"id":"https://openalex.org/C125792925","wikidata":"https://www.wikidata.org/wiki/Q3115604","display_name":"Outerplanar graph","level":5,"score":0.6233638525009155},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6061890721321106},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5902789831161499},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.5881271958351135},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5594409704208374},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.5167876482009888},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.46517276763916016},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4643675684928894},{"id":"https://openalex.org/C91233654","wikidata":"https://www.wikidata.org/wiki/Q4555371","display_name":"Polyhedral graph","level":5,"score":0.4434836804866791},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.3514993190765381},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.336406409740448},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.30100017786026},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2269999384880066},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0549299418926239},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-0-8176-4904-3_2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-0-8176-4904-3_2","pdf_url":null,"source":{"id":"https://openalex.org/S4306462921","display_name":"Birkh\u00e4user Boston eBooks","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":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Towards an Information Theory of Complex Networks","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W193938304","https://openalex.org/W1489554686","https://openalex.org/W1504530241","https://openalex.org/W1546271455","https://openalex.org/W1578476214","https://openalex.org/W1607543368","https://openalex.org/W1628980403","https://openalex.org/W1697214697","https://openalex.org/W1964700557","https://openalex.org/W1971148082","https://openalex.org/W1971404176","https://openalex.org/W1975373301","https://openalex.org/W1975570061","https://openalex.org/W1981505946","https://openalex.org/W1982538209","https://openalex.org/W1986970296","https://openalex.org/W1990921890","https://openalex.org/W1996008071","https://openalex.org/W2001161770","https://openalex.org/W2007576514","https://openalex.org/W2008516236","https://openalex.org/W2010356699","https://openalex.org/W2018165282","https://openalex.org/W2029630058","https://openalex.org/W2038643780","https://openalex.org/W2039498863","https://openalex.org/W2054600724","https://openalex.org/W2065527713","https://openalex.org/W2082230637","https://openalex.org/W2116365500","https://openalex.org/W2119115989","https://openalex.org/W2134147092","https://openalex.org/W2135368961","https://openalex.org/W2142636632","https://openalex.org/W2155929119","https://openalex.org/W2234861001","https://openalex.org/W2477674116","https://openalex.org/W2561675875","https://openalex.org/W2798588639","https://openalex.org/W2911393167"],"related_works":["https://openalex.org/W1759199114","https://openalex.org/W2995965358","https://openalex.org/W2009558719","https://openalex.org/W4327673321","https://openalex.org/W2963028755","https://openalex.org/W2338949323","https://openalex.org/W4298336578","https://openalex.org/W2045730620","https://openalex.org/W2184712314","https://openalex.org/W28463467"],"abstract_inverted_index":{"This":[0,93],"chapter":[1],"deals":[2],"with":[3],"compressed":[4],"coding":[5,141],"of":[6,17,38,40,61,84,113,121,142],"graphs.":[7,18,68,105,144],"We":[8,106,128],"focus":[9],"on":[10,67,77,110,118],"planar":[11,20,42,49,54,78,89,104,115,126,143],"graphs,":[12,50,79],"a":[13,23,41,53,82,85,124],"widely":[14],"studied":[15],"class":[16],"A":[19],"graph":[21,24,55],"is":[22],"that":[25],"admits":[26],"an":[27,58,73,97,131,139],"embedding":[28,87],"in":[29,123],"the":[30,111,119],"plane":[31],"without":[32],"edge":[33],"crossings.":[34],"Planar":[35],"maps":[36,136],"(class":[37],"embeddings":[39],"graph)":[43],"are":[44],"easier":[45],"to":[46,71,95,100,133],"study":[47,101],"than":[48],"but":[51],"as":[52],"may":[56],"admit":[57],"exponential":[59],"number":[60,112,120],"maps,":[62],"they":[63],"give":[64,72],"little":[65],"information":[66],"In":[69],"order":[70],"information-theoretic":[74],"upper":[75,108],"bound":[76],"we":[80],"introduce":[81],"definition":[83],"quasi-canonical":[86],"for":[88],"graphs:":[90],"well-orderly":[91,135],"maps.":[92],"appears":[94],"be":[96],"useful":[98],"tool":[99],"and":[102,117,137],"encode":[103],"present":[107,130],"bounds":[109],"unlabeled1":[114],"graphs":[116],"edges":[122],"random":[125],"graph.":[127],"also":[129],"algorithm":[132],"compute":[134],"implying":[138],"efficient":[140]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
