{"id":"https://openalex.org/W2726239457","doi":"https://doi.org/10.1007/s00454-018-0035-8","title":"A Proof of the Orbit Conjecture for Flipping Edge-Labelled Triangulations","display_name":"A Proof of the Orbit Conjecture for Flipping Edge-Labelled Triangulations","publication_year":2018,"publication_date":"2018-09-26","ids":{"openalex":"https://openalex.org/W2726239457","doi":"https://doi.org/10.1007/s00454-018-0035-8","mag":"2726239457"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-018-0035-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-018-0035-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-018-0035-8.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 & Computational Geometry","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-018-0035-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044299176","display_name":"Anna Lubiw","orcid":"https://orcid.org/0000-0002-2338-361X"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Anna Lubiw","raw_affiliation_strings":["School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada","School of Computer Science,, University of Waterloo, Waterloo, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"School of Computer Science,, University of Waterloo, Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016946629","display_name":"Zuzana Mas\u00e1rov\u00e1","orcid":"https://orcid.org/0000-0002-6660-1322"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Zuzana Mas\u00e1rov\u00e1","raw_affiliation_strings":["IST Austria, Am Campus 1, 3400, Klosterneuburg, Austria","IST Austria; Klosterneuburg Austria"],"raw_orcid":"https://orcid.org/0000-0002-6660-1322","affiliations":[{"raw_affiliation_string":"IST Austria, Am Campus 1, 3400, Klosterneuburg, Austria","institution_ids":["https://openalex.org/I157556583"]},{"raw_affiliation_string":"IST Austria; Klosterneuburg Austria","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056297132","display_name":"Uli Wagner","orcid":"https://orcid.org/0000-0002-1494-0568"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Uli Wagner","raw_affiliation_strings":["IST Austria, Am Campus 1, 3400, Klosterneuburg, Austria","IST Austria; Klosterneuburg Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IST Austria, Am Campus 1, 3400, Klosterneuburg, Austria","institution_ids":["https://openalex.org/I157556583"]},{"raw_affiliation_string":"IST Austria; Klosterneuburg Austria","institution_ids":["https://openalex.org/I157556583"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044299176"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02286591,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"61","issue":"4","first_page":"880","last_page":"898"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998000264167786,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998000264167786,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.998199999332428,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.996399998664856,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7586038708686829},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7223039865493774},{"id":"https://openalex.org/keywords/quadrilateral","display_name":"Quadrilateral","score":0.7170174717903137},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6641190052032471},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"Simplicial complex","score":0.6229641437530518},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.610835075378418},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.537031888961792},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5281448364257812},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5153172016143799},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.44980043172836304},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2093113362789154},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09568813443183899}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7586038708686829},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7223039865493774},{"id":"https://openalex.org/C151756577","wikidata":"https://www.wikidata.org/wiki/Q36810","display_name":"Quadrilateral","level":3,"score":0.7170174717903137},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6641190052032471},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.6229641437530518},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.610835075378418},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.537031888961792},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5281448364257812},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5153172016143799},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.44980043172836304},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2093113362789154},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09568813443183899},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1007/s00454-018-0035-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-018-0035-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-018-0035-8.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 & Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1710.02741","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.02741","pdf_url":"https://arxiv.org/pdf/1710.02741","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2726239457","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1710.02741","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:drops-oai.dagstuhl.de:7207","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.49","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"InProceedings"},{"id":"doi:10.48550/arxiv.1710.02741","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1710.02741","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"doi:10.4230/lipics.socg.2017.49","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.socg.2017.49","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""},{"id":"mag:2948460206","is_oa":false,"landing_page_url":"http://dblp.uni-trier.de/db/conf/compgeom/compgeom2017.html#LubiwMW17","pdf_url":null,"source":{"id":"https://openalex.org/S4306420969","display_name":"Symposium on Computational Geometry","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":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Symposium on Computational Geometry","raw_type":null}],"best_oa_location":{"id":"doi:10.1007/s00454-018-0035-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-018-0035-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-018-0035-8.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 & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320315473","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2726239457.pdf","grobid_xml":"https://content.openalex.org/works/W2726239457.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W269812687","https://openalex.org/W1496383623","https://openalex.org/W1542085343","https://openalex.org/W1571721549","https://openalex.org/W1591127925","https://openalex.org/W1659568777","https://openalex.org/W1797875829","https://openalex.org/W1977413884","https://openalex.org/W1987750368","https://openalex.org/W1990052191","https://openalex.org/W1997048861","https://openalex.org/W2005742663","https://openalex.org/W2019103912","https://openalex.org/W2022116663","https://openalex.org/W2029387472","https://openalex.org/W2050167630","https://openalex.org/W2061197783","https://openalex.org/W2089645963","https://openalex.org/W2110762325","https://openalex.org/W2163548699","https://openalex.org/W2172042336","https://openalex.org/W2263302607","https://openalex.org/W2500763296","https://openalex.org/W2528711716","https://openalex.org/W2560841694","https://openalex.org/W2912041544","https://openalex.org/W2962848607","https://openalex.org/W2963273558","https://openalex.org/W3102370784","https://openalex.org/W3104079118","https://openalex.org/W4237579241","https://openalex.org/W4254205555"],"related_works":["https://openalex.org/W2963015257","https://openalex.org/W2006109394","https://openalex.org/W2079428457","https://openalex.org/W2182726087","https://openalex.org/W1489961886","https://openalex.org/W3089134820","https://openalex.org/W1991884410","https://openalex.org/W2107975212","https://openalex.org/W2963667153","https://openalex.org/W2804024573","https://openalex.org/W3100672473","https://openalex.org/W2768412236","https://openalex.org/W1528971596","https://openalex.org/W2103216985","https://openalex.org/W2105550682","https://openalex.org/W2280201371","https://openalex.org/W3118940885","https://openalex.org/W2908564870","https://openalex.org/W2145386666","https://openalex.org/W2527935502"],"abstract_inverted_index":{"Given":[0],"a":[1,4,10,19,40,66,69,72,94,106,216,222,230,243,275,280,287,293,301,306],"triangulation":[2,38,49,67,92,104,136,238],"of":[3,29,39,53,65,77,93,108,153,232,252,257,270,295,313,332,335],"point":[5,41,95,277],"set":[6,42,96,278],"in":[7,59,133,143],"the":[8,26,30,60,75,78,82,134,144,173,226,255,258,264,268,318,322,333,336,341],"plane,":[9],"flip":[11,73,259,319,324,337],"deletes":[12],"an":[13,119,249],"edge":[14,64,80,128,138],"e":[15,24,129,160],"whose":[16],"removal":[17],"leaves":[18],"convex":[20],"quadrilateral,":[21],"and":[22,71,137,170,197,246,297],"replaces":[23],"by":[25,50],"opposite":[27],"diagonal":[28],"quadrilateral.":[31],"It":[32,85],"is":[33,86,115,118,182,284],"well":[34],"known":[35],"that":[36,89,155,178,186,267,283],"any":[37,47],"can":[43,97,189,203],"be":[44,98,150,190,204],"reconfigured":[45,99],"to":[46,81,100,161,193,206,228,234,239,286,339],"other":[48,102,165],"some":[51,151],"sequence":[52,107,152,231,244],"flips.":[54],"We":[55,209,329],"explore":[56],"this":[57,114,179,211,314],"question":[58],"setting":[61],"where":[62],"each":[63,124,200],"has":[68,130,140,321],"label,":[70],"transfers":[74],"label":[76,125,131,141,157,201],"removed":[79],"new":[83],"edge.":[84],"not":[87],"true":[88],"every":[90,101],"labelled":[91,103,237],"via":[105],"flips,":[109],"but":[110],"we":[111,214,247,299],"characterize":[112],"when":[113],"possible.":[116],"There":[117],"obvious":[120],"necessary":[121,180],"condition:":[122],"for":[123],"l,":[126],"if":[127,196,199,241],"l":[132,142,158],"first":[135],"f":[139],"second":[145],"triangulation,":[146],"then":[147],"there":[148],"must":[149],"flips":[154,233],"moves":[156],"from":[159,292],"f,":[162],"ignoring":[163],"all":[164,187],"labels.":[166],"Bose,":[167],"Lubiw,":[168],"Pathak":[169],"Verdonschot":[171],"formulated":[172],"Orbit":[174,342],"Conjecture,":[175],"which":[176],"states":[177],"condition":[181],"also":[183],"sufficient,":[184],"i.e.":[185],"labels":[188],"simultaneously":[191],"mapped":[192,205],"their":[194],"destination":[195],"only":[198],"individually":[202],"its":[207,327],"destination.":[208],"prove":[210,248,340],"conjecture.":[212],"Furthermore,":[213],"give":[215,300],"polynomial-time":[217],"algorithm":[218],"(with":[219],"$$O(n^8)$$":[220],"being":[221],"crude":[223],"bound":[224,251],"on":[225,254,274,305],"run-time)":[227],"find":[229],"reconfigure":[235],"one":[236],"another,":[240],"such":[242],"exists,":[245],"upper":[250],"$$O(n^7)$$":[253],"length":[256],"sequence.":[260],"Our":[261],"proof":[262,303],"uses":[263],"topological":[265],"result":[266,294],"sets":[269],"pairwise":[271],"non-crossing":[272],"edges":[273],"planar":[276],"form":[279],"simplicial":[281,315],"complex":[282,312,338],"homeomorphic":[285],"high-dimensional":[288],"ball":[289],"(this":[290],"follows":[291],"Orden":[296],"Santos;":[298],"different":[302],"based":[304],"shelling":[307],"argument).":[308],"The":[309],"dual":[310],"cell":[311],"ball,":[316],"called":[317],"complex,":[320],"usual":[323],"graph":[325],"as":[326],"1-skeleton.":[328],"use":[330],"properties":[331],"2-skeleton":[334],"Conjecture.":[343]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}