{"id":"https://openalex.org/W7163896035","doi":"https://doi.org/10.4230/lipics.swat.2026.33","title":"Polychromatic 2-Colorings with Bounded Discrepancy for Triangulations","display_name":"Polychromatic 2-Colorings with Bounded Discrepancy for Triangulations","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7163896035","doi":"https://doi.org/10.4230/lipics.swat.2026.33"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:26069","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.33","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol370-swat2026/LIPIcs.SWAT.2026.33/LIPIcs.SWAT.2026.33.pdf","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":null,"raw_type":"publishedVersion"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol370-swat2026/LIPIcs.SWAT.2026.33/LIPIcs.SWAT.2026.33.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138131886","display_name":"Alma Arevalo Loyola","orcid":"https://orcid.org/0009-0007-4618-2718"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Loyola, Alma Arevalo","raw_affiliation_strings":["School of Computer Science, Carleton University, Ottawa, Canada"],"raw_orcid":"https://orcid.org/0009-0007-4618-2718","affiliations":[{"raw_affiliation_string":"School of Computer Science, Carleton University, Ottawa, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015212072","display_name":"Ahmad Biniaz","orcid":"https://orcid.org/0000-0002-6396-4494"},"institutions":[{"id":"https://openalex.org/I74413500","display_name":"University of Windsor","ror":"https://ror.org/01gw3d370","country_code":"CA","type":"education","lineage":["https://openalex.org/I74413500"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Biniaz, Ahmad","raw_affiliation_strings":["School of Computer Science, University of Windsor, Canada"],"raw_orcid":"https://orcid.org/0000-0002-6396-4494","affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Windsor, Canada","institution_ids":["https://openalex.org/I74413500"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137171323","display_name":"Prosenjit Bose","orcid":"https://orcid.org/0000-0002-8906-0573"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Bose, Prosenjit","raw_affiliation_strings":["School of Computer Science, Carleton University, Ottawa, Canada"],"raw_orcid":"https://orcid.org/0000-0002-8906-0573","affiliations":[{"raw_affiliation_string":"School of Computer Science, Carleton University, Ottawa, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5097183224","display_name":"Thomas Shermer","orcid":null},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Shermer, Thomas","raw_affiliation_strings":["School of Computing Science, Simon Fraser University, Burnaby, Canada"],"raw_orcid":"https://orcid.org/0000-0003-3662-4870","affiliations":[{"raw_affiliation_string":"School of Computing Science, Simon Fraser University, Burnaby, Canada","institution_ids":["https://openalex.org/I18014758"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.94034918,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.7588000297546387,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.7588000297546387,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.07760000228881836,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.029600000008940697,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/delaunay-triangulation","display_name":"Delaunay triangulation","score":0.8668000102043152},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.6617000102996826},{"id":"https://openalex.org/keywords/pitteway-triangulation","display_name":"Pitteway triangulation","score":0.640999972820282},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5907999873161316},{"id":"https://openalex.org/keywords/point-set-triangulation","display_name":"Point set triangulation","score":0.5203999876976013},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4641000032424927},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4325999915599823}],"concepts":[{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.8668000102043152},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7799999713897705},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7139999866485596},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.6617000102996826},{"id":"https://openalex.org/C178609930","wikidata":"https://www.wikidata.org/wiki/Q3538712","display_name":"Pitteway triangulation","level":3,"score":0.640999972820282},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5907999873161316},{"id":"https://openalex.org/C167117609","wikidata":"https://www.wikidata.org/wiki/Q17078161","display_name":"Point set triangulation","level":3,"score":0.5203999876976013},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4641000032424927},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4325999915599823},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3765999972820282},{"id":"https://openalex.org/C121198538","wikidata":"https://www.wikidata.org/wiki/Q4951461","display_name":"Bowyer\u2013Watson algorithm","level":3,"score":0.32690000534057617},{"id":"https://openalex.org/C128321387","wikidata":"https://www.wikidata.org/wiki/Q5164356","display_name":"Constrained Delaunay triangulation","level":3,"score":0.3158000111579895},{"id":"https://openalex.org/C39969762","wikidata":"https://www.wikidata.org/wiki/Q6865406","display_name":"Minimum-weight triangulation","level":4,"score":0.29649999737739563},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.2865000069141388},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.271699994802475},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2651999890804291}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:26069","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.33","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol370-swat2026/LIPIcs.SWAT.2026.33/LIPIcs.SWAT.2026.33.pdf","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":null,"raw_type":"publishedVersion"},{"id":"doi:10.4230/lipics.swat.2026.33","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.swat.2026.33","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":""}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:26069","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.33","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol370-swat2026/LIPIcs.SWAT.2026.33/LIPIcs.SWAT.2026.33.pdf","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":null,"raw_type":"publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7163896035.pdf","grobid_xml":"https://content.openalex.org/works/W7163896035.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0],"polychromatic":[1,47,65,92],"2-coloring":[2,8,48,66,93,102,148],"of":[3,9,20,30,60,79,114,123,136],"a":[4,7,21,46,58,91,101,112,121,134,142,147],"triangulation":[5,44,89],"is":[6,16,23,76,151],"the":[10,24,28,31,77,83],"vertices":[11],"such":[12,100],"that":[13,42,55,87,130],"no":[14],"face":[15],"monochromatic.":[17],"The":[18],"discrepancy":[19,50,68,95,113,135,150],"coloring":[22],"maximum":[25],"difference":[26],"between":[27],"sizes":[29],"color":[32],"classes.":[33],"Asayama":[34],"and":[35,38,54,99],"Matsumoto":[36],"(Graphs":[37],"Combinatorics,":[39],"2022)":[40],"proved":[41],"every":[43,64,88],"admits":[45,90],"with":[49,94,120],"at":[51,69,96,115,137,152],"most":[52,97,116,138,153],"(5n-16)/9,":[53],"there":[56],"exists":[57],"class":[59],"triangulations":[61,119,132],"for":[62,118,128],"which":[63],"has":[67],"least":[70],"n/3":[71],"-":[72],"2,":[73],"where":[74],"n":[75],"number":[78],"vertices.":[80],"We":[81,109,140],"improve":[82],"upper":[84],"bound,":[85],"showing":[86],"(3n-16)/7":[98],"can":[103],"be":[104],"computed":[105],"in":[106],"quadratic":[107],"time.":[108],"also":[110],"show":[111],"n-4M/3":[117],"matching":[122],"size":[124],"M.":[125],"This":[126],"implies,":[127],"example,":[129],"Delaunay":[131],"admit":[133],"n/3.":[139],"provide":[141],"linear-time":[143],"algorithm":[144],"to":[145],"compute":[146],"whose":[149],"(5n-24)/7.":[154]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-06-09T00:00:00"}