{"id":"https://openalex.org/W1489491179","doi":"https://doi.org/10.37236/1437","title":"Orthogonal Colorings of Graphs","display_name":"Orthogonal Colorings of Graphs","publication_year":1998,"publication_date":"1998-12-06","ids":{"openalex":"https://openalex.org/W1489491179","doi":"https://doi.org/10.37236/1437","mag":"1489491179"},"language":"en","primary_location":{"id":"doi:10.37236/1437","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1437","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v6i1r5/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v6i1r5/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000697501","display_name":"Yair Caro","orcid":"https://orcid.org/0000-0002-9687-5770"},"institutions":[{"id":"https://openalex.org/I107326029","display_name":"Oranim Academic College of Education","ror":"https://ror.org/01539v588","country_code":"IL","type":"education","lineage":["https://openalex.org/I107326029"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Yair Caro","raw_affiliation_strings":["Department of Mathematics University of Haifa-ORANIM, Tivon 36006, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Haifa-ORANIM, Tivon 36006, Israel","institution_ids":["https://openalex.org/I107326029"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026016357","display_name":"Raphael Yuster","orcid":"https://orcid.org/0000-0001-7550-6506"},"institutions":[{"id":"https://openalex.org/I107326029","display_name":"Oranim Academic College of Education","ror":"https://ror.org/01539v588","country_code":"IL","type":"education","lineage":["https://openalex.org/I107326029"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Raphael Yuster","raw_affiliation_strings":["Department of Mathematics University of Haifa-ORANIM, Tivon 36006, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Haifa-ORANIM, Tivon 36006, Israel","institution_ids":["https://openalex.org/I107326029"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5000697501"],"corresponding_institution_ids":["https://openalex.org/I107326029"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.04229844,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"6","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"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":0.9979000091552734,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9976999759674072,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.9180318117141724},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.82811439037323},{"id":"https://openalex.org/keywords/greedy-coloring","display_name":"Greedy coloring","score":0.5735043883323669},{"id":"https://openalex.org/keywords/fractional-coloring","display_name":"Fractional coloring","score":0.5718153715133667},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5604835748672485},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.5525979399681091},{"id":"https://openalex.org/keywords/complete-coloring","display_name":"Complete coloring","score":0.5452682375907898},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.5052281022071838},{"id":"https://openalex.org/keywords/list-coloring","display_name":"List coloring","score":0.4974217712879181},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47085732221603394},{"id":"https://openalex.org/keywords/orthogonal-array","display_name":"Orthogonal array","score":0.4393312931060791},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3669009506702423},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.15778693556785583}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9180318117141724},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.82811439037323},{"id":"https://openalex.org/C38767284","wikidata":"https://www.wikidata.org/wiki/Q5601715","display_name":"Greedy coloring","level":5,"score":0.5735043883323669},{"id":"https://openalex.org/C158319403","wikidata":"https://www.wikidata.org/wiki/Q5477527","display_name":"Fractional coloring","level":5,"score":0.5718153715133667},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5604835748672485},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.5525979399681091},{"id":"https://openalex.org/C21642379","wikidata":"https://www.wikidata.org/wiki/Q3342988","display_name":"Complete coloring","level":5,"score":0.5452682375907898},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5052281022071838},{"id":"https://openalex.org/C199594403","wikidata":"https://www.wikidata.org/wiki/Q1130404","display_name":"List coloring","level":5,"score":0.4974217712879181},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47085732221603394},{"id":"https://openalex.org/C42632107","wikidata":"https://www.wikidata.org/wiki/Q2031860","display_name":"Orthogonal array","level":3,"score":0.4393312931060791},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3669009506702423},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.15778693556785583},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C83469408","wikidata":"https://www.wikidata.org/wiki/Q2036525","display_name":"Taguchi methods","level":2,"score":0.0},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/1437","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1437","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v6i1r5/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.31.5375","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.5375","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.tau.ac.il/~raphy/orthcol.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.44.5703","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.44.5703","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_6/PostScriptfiles/v6i1r5.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.46.4500","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.4500","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mi.sanu.ac.yu/EMIS/journals/EJC/Volume_6/PDF/v6i1r5.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1437","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1437","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v6i1r5/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1489491179.pdf","grobid_xml":"https://content.openalex.org/works/W1489491179.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W403078265","https://openalex.org/W1510730180","https://openalex.org/W1990479896","https://openalex.org/W2010354676","https://openalex.org/W2483090012","https://openalex.org/W6814508481"],"related_works":["https://openalex.org/W2042876012","https://openalex.org/W2151059773","https://openalex.org/W2376326396","https://openalex.org/W1974068132","https://openalex.org/W2353563269","https://openalex.org/W2356152809","https://openalex.org/W4288274833","https://openalex.org/W2365539738","https://openalex.org/W2056389765","https://openalex.org/W1489491179"],"abstract_inverted_index":{"An":[0],"orthogonal":[1,42,51,55,73,102,127,196,211,220],"coloring":[2,74,103],"of":[3,11,14,41,50,58,68,75,154,189,203,219],"a":[4,8,125],"graph":[5,173],"$G$":[6,78,95,123],"is":[7,44,63,96,115,138,157],"pair":[9],"$\\{c_1,c_2\\}$":[10],"proper":[12],"colorings":[13,43],"$G$,":[15,59],"having":[16,191],"the":[17,26,48,64,83,160,177,181,187,216,227],"property":[18],"that":[19,86,122,200],"if":[20,104],"two":[21,132],"vertices":[22],"are":[23],"colored":[24,142],"with":[25],"same":[27,228],"color":[28,229],"in":[29,37,71,112,145,150,230],"$c_1$,":[30],"then":[31,82,119],"they":[32],"must":[33],"have":[34,99,206],"distinct":[35],"colors":[36,69,133],"$c_2$.":[38,151],"The":[39,54,152],"notion":[40,49],"strongly":[45],"related":[46],"to":[47,98,158,167],"Latin":[52],"squares.":[53],"chromatic":[56,182],"number":[57,67],"denoted":[60],"by":[61,143,148],"$O\\chi(G)$,":[62],"minimum":[65],"possible":[66],"used":[70],"an":[72,100,116,192,207],"$G$.":[76],"If":[77],"has":[79,124],"$n$":[80,114],"vertices,":[81],"definition":[84],"implies":[85],"$\\left\\lceil":[87],"\\sqrt{n}":[88,108],"\\,":[89,109],"\\right\\rceil":[90],"\\leq":[91,93],"O\\chi(G)":[92],"n$.":[94],"said":[97],"optimal":[101,193,208],"$O\\chi(G)":[105],"=":[106],"\\left\\lceil":[107],"\\right\\rceil$.":[110],"If,":[111],"addition,":[113],"integer":[117],"square,":[118],"we":[120],"say":[121],"perfect":[126,195,210],"coloring,":[128,197],"since":[129],"for":[130],"any":[131],"$x$":[134,144],"and":[135,147,163,180,198],"$y$,":[136],"there":[137],"exactly":[139],"one":[140],"vertex":[141,224],"$c_1$":[146],"$y$":[149],"purpose":[153],"this":[155],"paper":[156],"study":[159,186],"parameter":[161],"$O\\chi(G)$":[162],"supply":[164],"upper":[165],"bounds":[166],"it":[168],"which":[169],"depend":[170],"on":[171],"other":[172],"parameters":[174],"such":[175],"as":[176],"maximum":[178],"degree":[179],"number.":[183],"We":[184,213],"also":[185,214],"structure":[188],"graphs":[190,204],"or":[194,209],"show":[199],"several":[201],"classes":[202],"always":[205],"coloring.":[212],"consider":[215],"strong":[217],"version":[218],"colorings,":[221],"where":[222],"no":[223],"may":[225],"receive":[226],"both":[231],"colorings.":[232]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}