{"id":"https://openalex.org/W2972232919","doi":"https://doi.org/10.1007/s00373-020-02155-y","title":"2-Edge-Colored Chromatic Number of Grids is at Most 9","display_name":"2-Edge-Colored Chromatic Number of Grids is at Most 9","publication_year":2020,"publication_date":"2020-03-11","ids":{"openalex":"https://openalex.org/W2972232919","doi":"https://doi.org/10.1007/s00373-020-02155-y","mag":"2972232919"},"language":"lv","primary_location":{"id":"doi:10.1007/s00373-020-02155-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-020-02155-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-020-02155-y.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"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":"Graphs and Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00373-020-02155-y.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076869546","display_name":"Janusz Dybizba\u0144ski","orcid":"https://orcid.org/0000-0002-2575-4373"},"institutions":[{"id":"https://openalex.org/I40413290","display_name":"University of Gda\u0144sk","ror":"https://ror.org/011dv8m48","country_code":"PL","type":"education","lineage":["https://openalex.org/I40413290"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Janusz Dybizba\u0144ski","raw_affiliation_strings":["Institute of Informatics, Faculty of Mathematics, Physics and Informatics, University of Gda\u0144sk, 80-308, Gda\u0144sk, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Informatics, Faculty of Mathematics, Physics and Informatics, University of Gda\u0144sk, 80-308, Gda\u0144sk, Poland","institution_ids":["https://openalex.org/I40413290"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5076869546"],"corresponding_institution_ids":["https://openalex.org/I40413290"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.4332,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.66819123,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"36","issue":"3","first_page":"831","last_page":"837"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9925000071525574,"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/T10849","display_name":"Finite Group Theory Research","score":0.9900000095367432,"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/algorithm","display_name":"Algorithm","score":0.49635201692581177},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3235769271850586},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3035416603088379}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49635201692581177},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3235769271850586},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3035416603088379}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00373-020-02155-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-020-02155-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-020-02155-y.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"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":"Graphs and Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1909.00371","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.00371","pdf_url":"https://arxiv.org/pdf/1909.00371","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"}],"best_oa_location":{"id":"doi:10.1007/s00373-020-02155-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-020-02155-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-020-02155-y.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"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":"Graphs and Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2972232919.pdf","grobid_xml":"https://content.openalex.org/works/W2972232919.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1504781213","https://openalex.org/W2004852774","https://openalex.org/W2057216953","https://openalex.org/W2114043019","https://openalex.org/W2168040452","https://openalex.org/W2441249653","https://openalex.org/W2508099963","https://openalex.org/W2963649630","https://openalex.org/W2976668395","https://openalex.org/W3040730123","https://openalex.org/W4312889685"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626"],"abstract_inverted_index":{"Abstract":[0],"A":[1,36],"2-edge-colored":[2,37,41,53,62,67,108,117,122,144,149],"graph":[3,42,54,68,110],"is":[4,14,27,48,74,124,154],"a":[5,15,28,49,52,98],"pair":[6],"$$(G,":[7,43,69,91,101],"\\sigma":[8,44,70,92,102],")$$":[9,45,57,71,93,103],"<mml:math":[10,25,46,58,72,94,104,112],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mo>(</mml:mo><mml:mi>G</mml:mi><mml:mo>,</mml:mo><mml:mi>\u03c3</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>":[11,47,73,95,105],"where":[12],"G":[13],"graph,":[16],"and":[17],"$$\\sigma":[18],":E(G)\\rightarrow":[19],"\\{\\text":[20],"{'}+\\text":[21],"{'},\\text":[22],"{'}-\\text":[23],"{'}\\}$$":[24],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>\u03c3</mml:mi><mml:mo>:</mml:mo><mml:mi>E</mml:mi><mml:mo>(</mml:mo><mml:mi>G</mml:mi><mml:mo>)</mml:mo><mml:mo>\u2192</mml:mo><mml:mo>{</mml:mo><mml:mtext>'</mml:mtext><mml:mo>+</mml:mo><mml:mtext>'</mml:mtext><mml:mo>,</mml:mo><mml:mtext>'</mml:mtext><mml:mo>-</mml:mo><mml:mtext>'</mml:mtext><mml:mo>}</mml:mo></mml:mrow></mml:math>":[26],"function":[29],"which":[30],"marks":[31],"all":[32],"edges":[33],"with":[34,151],"signs.":[35],"coloring":[38],"of":[39,65,78,120,147],"the":[40,66,75,107,116,121,130,148],"homomorphism":[50,99],"into":[51,106],"$$(H,":[55],"\\delta":[56],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mo>(</mml:mo><mml:mi>H</mml:mi><mml:mo>,</mml:mo><mml:mi>\u03b4</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>":[59],".":[60,80,114],"The":[61],"chromatic":[63,118,145],"number":[64,119,135,146],"minimum":[76],"order":[77],"H":[79],"In":[81],"this":[82,134],"paper":[83],"we":[84,141],"show":[85,142],"that":[86,143],"for":[87],"every":[88],"2-dimensional":[89],"grid":[90],"there":[96],"exists":[97],"from":[100],"Paley":[109],"$$SP_9$$":[111],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>S</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mn>9</mml:mn></mml:msub></mml:mrow></mml:math>":[113],"Hence,":[115],"grids":[123,150],"at":[125,155],"most":[126,156],"9.":[127],"This":[128],"improves":[129],"upper":[131],"bound":[132],"on":[133],"obtained":[136],"recently":[137],"by":[138],"Bensmail.":[139],"Additionally,":[140],"3":[152],"columns":[153],"8.":[157]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2019-09-12T00:00:00"}
