{"id":"https://openalex.org/W4360978585","doi":"https://doi.org/10.1007/s00454-023-00494-0","title":"Tutte Embeddings of Tetrahedral Meshes","display_name":"Tutte Embeddings of Tetrahedral Meshes","publication_year":2023,"publication_date":"2023-03-17","ids":{"openalex":"https://openalex.org/W4360978585","doi":"https://doi.org/10.1007/s00454-023-00494-0"},"language":"lv","primary_location":{"id":"doi:10.1007/s00454-023-00494-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-023-00494-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00494-0.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00494-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072827199","display_name":"Marc Alexa","orcid":"https://orcid.org/0000-0002-9854-8466"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Marc Alexa","raw_affiliation_strings":["Faculty of Computer Science & Electrical Engineering, TU Berlin, Sekretariat MAR 6-6, Marchstr. 6, 10587, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0002-9854-8466","affiliations":[{"raw_affiliation_string":"Faculty of Computer Science & Electrical Engineering, TU Berlin, Sekretariat MAR 6-6, Marchstr. 6, 10587, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5072827199"],"corresponding_institution_ids":["https://openalex.org/I4577782"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.9245,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.8969555,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"73","issue":"1","first_page":"197","last_page":"207"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998000264167786,"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":0.9998000264167786,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9990000128746033,"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/T11870","display_name":"Structural Analysis and Optimization","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/combinatorics","display_name":"Combinatorics","score":0.7936902642250061},{"id":"https://openalex.org/keywords/polyhedral-graph","display_name":"Polyhedral graph","score":0.7886122465133667},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.705467700958252},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.6700052618980408},{"id":"https://openalex.org/keywords/tetrahedron","display_name":"Tetrahedron","score":0.6473742127418518},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5424582958221436},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.49686554074287415},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.4782347083091736},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.4760065972805023},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3899305462837219},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2887610197067261},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.2848045825958252},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.13944292068481445},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09966501593589783},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.08244279026985168},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.07352849841117859}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7936902642250061},{"id":"https://openalex.org/C91233654","wikidata":"https://www.wikidata.org/wiki/Q4555371","display_name":"Polyhedral graph","level":5,"score":0.7886122465133667},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.705467700958252},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.6700052618980408},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.6473742127418518},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5424582958221436},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.49686554074287415},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.4782347083091736},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.4760065972805023},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3899305462837219},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2887610197067261},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.2848045825958252},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.13944292068481445},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09966501593589783},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.08244279026985168},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.07352849841117859},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-023-00494-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-023-00494-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00494-0.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00454-023-00494-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-023-00494-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00494-0.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1372115314","display_name":null,"funder_award_id":"EXC-2046","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G2117824717","display_name":null,"funder_award_id":"project ID: 390685689","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G2990895770","display_name":null,"funder_award_id":"EXC-2046/1, project ID: 390685689","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3568794162","display_name":null,"funder_award_id":"EXC-2046/1, project ID: 390685689","funder_id":"https://openalex.org/F4320330291","funder_display_name":"Berlin Mathematics Research Center MATH+"},{"id":"https://openalex.org/G3684656814","display_name":null,"funder_award_id":"MATH+ (EXC-2046/1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6766639804","display_name":"Geometry Processing as Inference","funder_award_id":"101055448","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7354608348","display_name":null,"funder_award_id":"EXC-2046/1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7362566262","display_name":null,"funder_award_id":"EXC-2046/1","funder_id":"https://openalex.org/F4320330291","funder_display_name":"Berlin Mathematics Research Center MATH+"},{"id":"https://openalex.org/G7725451807","display_name":null,"funder_award_id":"390685689","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7842005466","display_name":null,"funder_award_id":"Horizon 2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8964763783","display_name":null,"funder_award_id":"390685689","funder_id":"https://openalex.org/F4320330291","funder_display_name":"Berlin Mathematics Research Center MATH+"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320330291","display_name":"Berlin Mathematics Research Center MATH+","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4360978585.pdf"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W2046729013","https://openalex.org/W2052259760","https://openalex.org/W2054363014","https://openalex.org/W2058639681","https://openalex.org/W2077000413","https://openalex.org/W2082388593","https://openalex.org/W2094366023","https://openalex.org/W2123858814","https://openalex.org/W2214452484","https://openalex.org/W2227413268","https://openalex.org/W2465272462","https://openalex.org/W2552221052","https://openalex.org/W2963924109"],"related_works":["https://openalex.org/W2081273953","https://openalex.org/W2963028755","https://openalex.org/W4239346727","https://openalex.org/W2017158410","https://openalex.org/W2078415120","https://openalex.org/W2886427884","https://openalex.org/W3002491985","https://openalex.org/W4224925562","https://openalex.org/W4240422189","https://openalex.org/W2022451101"],"abstract_inverted_index":{"Abstract":[0],"Tutte\u2019s":[1],"embedding":[2],"theorem":[3],"states":[4],"that":[5,63,107],"every":[6],"3-connected":[7],"graph":[8,109],"without":[9],"a":[10,35,73],"$$K_5$$":[11],"<mml:math":[12,22,117,127],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[13,23,118,128],"<mml:msub>":[14,24,119,129],"<mml:mi>K</mml:mi>":[15,25,120,130],"<mml:mn>5</mml:mn>":[16],"</mml:msub>":[17,31,122,138],"</mml:math>":[18,32,123,139],"-":[19],"or":[20],"$$K_{3,3}$$":[21],"<mml:mrow>":[26,131],"<mml:mn>3</mml:mn>":[27,29,132,134],"<mml:mo>,</mml:mo>":[28,133,135],"</mml:mrow>":[30,137],"-minor":[33],"(i.e.,":[34],"planar":[36],"graph)":[37],"is":[38,47,87,102],"embedded":[39,82],"in":[40,48,72,88],"the":[41,44,52,77,84,92,108,111],"plane":[42],"if":[43,83],"outer":[45,85],"face":[46],"convex":[49,56,89,96],"position":[50,90],"and":[51,91,124,141],"interior":[53,93],"vertices":[54,94,148],"are":[55,95,149],"combinations":[57],"of":[58,98,110],"their":[59,99],"neighbors.":[60],"We":[61],"show":[62],"this":[64],"result":[65],"extends":[66],"to":[67,80],"simply":[68],"connected":[69],"tetrahedral":[70,78,112],"meshes":[71],"natural":[74],"way:":[75],"for":[76],"mesh":[79,113],"be":[81],"polyhedron":[86],"combination":[97],"neighbors":[100],"it":[101],"sufficient":[103],"(but":[104],"not":[105],"necessary)":[106],"contains":[114],"no":[115,125],"$$K_6$$":[116],"<mml:mn>6</mml:mn>":[121],"$$K_{3,3,1}$$":[126],"<mml:mn>1</mml:mn>":[136],",":[140],"all":[142],"triangles":[143],"incident":[144],"on":[145],"three":[146],"boundary":[147,150],"triangles.":[151]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-05-19T08:33:51.333923","created_date":"2025-10-10T00:00:00"}
