{"id":"https://openalex.org/W3021406699","doi":"https://doi.org/10.1142/s0129054105002905","title":"CANONICAL DECOMPOSITION, REALIZER, SCHNYDER LABELING AND ORDERLY SPANNING TREES OF PLANE GRAPHS","display_name":"CANONICAL DECOMPOSITION, REALIZER, SCHNYDER LABELING AND ORDERLY SPANNING TREES OF PLANE GRAPHS","publication_year":2005,"publication_date":"2005-02-01","ids":{"openalex":"https://openalex.org/W3021406699","doi":"https://doi.org/10.1142/s0129054105002905","mag":"3021406699"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054105002905","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054105002905","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","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/A5108354107","display_name":"Kazuyuki Miura","orcid":null},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"KAZUYUKI MIURA","raw_affiliation_strings":["Graduate School of Information Sciences, Tohoku University, Aoba-yama 05, Sendai 980-8579, Japan"],"affiliations":[{"raw_affiliation_string":"Graduate School of Information Sciences, Tohoku University, Aoba-yama 05, Sendai 980-8579, Japan","institution_ids":["https://openalex.org/I201537933"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078769863","display_name":"Machiko Azuma","orcid":null},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"MACHIKO AZUMA","raw_affiliation_strings":["Graduate School of Information Sciences, Tohoku University, Aoba-yama 05, Sendai 980-8579, Japan"],"affiliations":[{"raw_affiliation_string":"Graduate School of Information Sciences, Tohoku University, Aoba-yama 05, Sendai 980-8579, Japan","institution_ids":["https://openalex.org/I201537933"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033580185","display_name":"Takao Nishizeki","orcid":null},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"TAKAO NISHIZEKI","raw_affiliation_strings":["Graduate School of Information Sciences, Tohoku University, Aoba-yama 05, Sendai 980-8579, Japan"],"affiliations":[{"raw_affiliation_string":"Graduate School of Information Sciences, Tohoku University, Aoba-yama 05, Sendai 980-8579, Japan","institution_ids":["https://openalex.org/I201537933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5108354107"],"corresponding_institution_ids":["https://openalex.org/I201537933"],"apc_list":null,"apc_paid":null,"fwci":2.2763,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.89675239,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"16","issue":"01","first_page":"117","last_page":"141"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11106","display_name":"Data Management and Algorithms","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/combinatorics","display_name":"Combinatorics","score":0.6898816823959351},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.6888836622238159},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.674460768699646},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.532020092010498},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.5027370452880859},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5005645751953125},{"id":"https://openalex.org/keywords/minimum-spanning-tree","display_name":"Minimum spanning tree","score":0.45633381605148315},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.4528326988220215},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.42598438262939453},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.346259742975235},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1390845775604248}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6898816823959351},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.6888836622238159},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.674460768699646},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.532020092010498},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.5027370452880859},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5005645751953125},{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.45633381605148315},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.4528326988220215},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.42598438262939453},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.346259742975235},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1390845775604248}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129054105002905","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054105002905","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7699999809265137,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W193938304","https://openalex.org/W619755549","https://openalex.org/W1574212655","https://openalex.org/W1964716955","https://openalex.org/W1994556169","https://openalex.org/W2003525146","https://openalex.org/W2010758649","https://openalex.org/W2038318850","https://openalex.org/W2045870980","https://openalex.org/W2062622930","https://openalex.org/W2082388593","https://openalex.org/W2120892678","https://openalex.org/W2123300935","https://openalex.org/W2289065784","https://openalex.org/W3104537554"],"related_works":["https://openalex.org/W2159421784","https://openalex.org/W2121473031","https://openalex.org/W4296605418","https://openalex.org/W2022010596","https://openalex.org/W2062226917","https://openalex.org/W3123513344","https://openalex.org/W3015472988","https://openalex.org/W1414065628","https://openalex.org/W123718951","https://openalex.org/W2029772672"],"abstract_inverted_index":{"A":[0],"canonical":[1,71],"decomposition,":[2,72],"a":[3,5,14,39,59,70,73,75,107],"realizer,":[4,74],"Schnyder":[6,76],"labeling":[7],"and":[8,48,61,67,82],"an":[9,18,78,83],"orderly":[10,79],"spanning":[11,80],"tree":[12],"of":[13],"plane":[15,108],"graph":[16,29,109],"play":[17],"important":[19],"role":[20],"in":[21,103],"straight-line":[22],"grid":[23,26,87],"drawings,":[24,27],"convex":[25,86],"floor-plannings,":[28],"encoding,":[30],"etc.":[31],"It":[32],"is":[33,38],"known":[34],"that":[35,69,98],"the":[36,111],"triconnectivity":[37],"sufficient":[40,49,62],"condition":[41,50,63],"for":[42,64],"their":[43,65],"existence,":[44,66],"but":[45],"no":[46],"necessary":[47,60],"has":[51],"been":[52],"known.":[53],"In":[54],"this":[55],"paper,":[56],"we":[57],"present":[58],"show":[68,97],"labeling,":[77],"tree,":[81],"outer":[84],"triangular":[85],"drawing":[88],"are":[89],"notions":[90],"equivalent":[91],"with":[92],"each":[93],"other.":[94],"We":[95],"also":[96],"they":[99],"can":[100],"be":[101],"found":[102],"linear":[104],"time":[105],"whenever":[106],"satisfies":[110],"condition.":[112]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
