{"id":"https://openalex.org/W4366677950","doi":"https://doi.org/10.1007/978-3-031-30823-9_20","title":"The Packing Chromatic Number of the Infinite Square Grid is 15","display_name":"The Packing Chromatic Number of the Infinite Square Grid is 15","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4366677950","doi":"https://doi.org/10.1007/978-3-031-30823-9_20"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-30823-9_20","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-30823-9_20","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-30823-9_20.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-30823-9_20.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030108071","display_name":"Bernardo Subercaseaux","orcid":"https://orcid.org/0000-0003-2295-1299"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Bernardo Subercaseaux","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA, 15203, USA"],"raw_orcid":"https://orcid.org/0000-0003-2295-1299","affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA, 15203, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025921874","display_name":"Marijn J. H. Heule","orcid":"https://orcid.org/0000-0002-5587-8801"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Marijn J. H. Heule","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA, 15203, USA"],"raw_orcid":"https://orcid.org/0000-0002-5587-8801","affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA, 15203, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030108071"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":9.4364,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.98353986,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"389","last_page":"406"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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/T10374","display_name":"Advanced Graph Theory Research","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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9980999827384949,"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":0.9973000288009644,"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/algorithm","display_name":"Algorithm","score":0.629006028175354},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5171727538108826},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.34252405166625977}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.629006028175354},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5171727538108826},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34252405166625977}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-031-30823-9_20","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-30823-9_20","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-30823-9_20.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/978-3-031-30823-9_20","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-30823-9_20","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-30823-9_20.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7352054642","display_name":"SHF: Small: WLoS: Without Loss of Satisfaction","funder_award_id":"2015445","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4366677950.pdf"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W66855977","https://openalex.org/W1496529478","https://openalex.org/W1656795039","https://openalex.org/W2017604542","https://openalex.org/W2021870295","https://openalex.org/W2027444730","https://openalex.org/W2119765243","https://openalex.org/W2483722158","https://openalex.org/W2590872906","https://openalex.org/W2797038806","https://openalex.org/W2954910840","https://openalex.org/W2998943866","https://openalex.org/W3017968798","https://openalex.org/W3095853283","https://openalex.org/W3185307588","https://openalex.org/W4366677950"],"related_works":["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/W2350741829","https://openalex.org/W2530322880"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"packing":[2,93,155],"k":[3,15],"-coloring":[4],"is":[5,147,181],"a":[6,45,72,86,148,178,191],"natural":[7],"variation":[8],"on":[9],"the":[10,92,97,113,128,196,200,203],"standard":[11,82],"notion":[12],"of":[13,88,96,138,193,202],"graph":[14,83],"-coloring,":[16],"where":[17],"vertices":[18,43],"are":[19,169],"assigned":[20,44],"numbers":[21],"from":[22],"$$\\{1,":[23],"\\ldots":[24,51],",":[25,39,52],"k\\}$$":[26,53],"<mml:math":[27,54],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[28,55],"<mml:mrow>":[29,56],"<mml:mo>{</mml:mo>":[30,59],"<mml:mn>1</mml:mn>":[31,60],"<mml:mo>,</mml:mo>":[32,34,61,63],"<mml:mo>\u2026</mml:mo>":[33,62],"<mml:mi>k</mml:mi>":[35,64],"<mml:mo>}</mml:mo>":[36,65],"</mml:mrow>":[37,66],"</mml:math>":[38,67],"and":[40],"any":[41],"two":[42,136],"common":[46],"color":[47],"$$c":[48],"\\in":[49],"\\{1,":[50],"<mml:mi>c</mml:mi>":[57],"<mml:mo>\u2208</mml:mo>":[58],"need":[68],"to":[69,79,119,144,183,199],"be":[70,120],"at":[71],"distance":[73],"greater":[74],"than":[75,172],"c":[76],"(as":[77],"opposed":[78],"1,":[80],"in":[81,109,190],"colorings).":[84],"Despite":[85],"sequence":[87],"incremental":[89],"work,":[90],"determining":[91],"chromatic":[94],"number":[95,118],"infinite":[98],"square":[99],"grid":[100],"has":[101],"remained":[102],"an":[103,160],"open":[104],"problem":[105,133],"since":[106],"its":[107],"introduction":[108],"2002.":[110],"We":[111,122,186],"culminate":[112],"search":[114],"by":[115,126,134],"proving":[116],"this":[117,124,132,176],"15.":[121],"achieve":[123],"result":[125],"improving":[127],"best-known":[129],"method":[130],"for":[131,154,175],"roughly":[135],"orders":[137],"magnitude.":[139],"The":[140],"most":[141],"important":[142],"technique":[143],"boost":[145],"performance":[146],"novel,":[149],"surprisingly":[150],"effective":[151],"propositional":[152],"encoding":[153],"colorings.":[156],"Additionally,":[157],"we":[158],"developed":[159],"alternative":[161],"symmetry":[162],"breaking":[163],"method.":[164],"Since":[165],"both":[166,188],"new":[167],"techniques":[168,174,189],"more":[170],"complex":[171],"existing":[173],"problem,":[177],"verified":[179],"approach":[180],"required":[182],"trust":[184],"them.":[185],"include":[187],"proof":[192],"unsatisfiability,":[194],"reducing":[195],"trusted":[197],"core":[198],"correctness":[201],"direct":[204],"encoding.":[205]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":2}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}
