{"id":"https://openalex.org/W7224999211","doi":"https://doi.org/10.5281/zenodo.23842785","title":"The geometric thickness of K14 is 4","display_name":"The geometric thickness of K14 is 4","publication_year":2026,"publication_date":"2026-10-31","ids":{"openalex":"https://openalex.org/W7224999211","doi":"https://doi.org/10.5281/zenodo.23842785"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23842785","doi":"https://doi.org/10.5281/zenodo.23842785","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23842785","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23842785","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5160045268","display_name":"Lee Marshall","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Marshall, Lee","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5160045268"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9502000212669373,"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":0.9502000212669373,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.02280000038444996,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.007799999788403511,"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/straight-line-drawings","display_name":"straight-line drawings","score":0.6349999904632568},{"id":"https://openalex.org/keywords/sat-encoding","display_name":"SAT encoding","score":0.5600000023841858},{"id":"https://openalex.org/keywords/unsatisfiability","display_name":"unsatisfiability","score":0.4350000023841858},{"id":"https://openalex.org/keywords/network-visualization","display_name":"network visualization","score":0.40700000524520874}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6682999730110168},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5795999765396118},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5756999850273132},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.5368000268936157},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.49619999527931213},{"id":"https://openalex.org/C7305733","wikidata":"https://www.wikidata.org/wiki/Q207961","display_name":"Geometric shape","level":2,"score":0.43070000410079956},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35519999265670776},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3409999907016754},{"id":"https://openalex.org/C118505674","wikidata":"https://www.wikidata.org/wiki/Q42586063","display_name":"Encoder","level":2,"score":0.3075999915599823},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C67666897","wikidata":"https://www.wikidata.org/wiki/Q165896","display_name":"Prism","level":2,"score":0.2590999901294708}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23842785","doi":"https://doi.org/10.5281/zenodo.23842785","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23842785","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23842786","doi":"https://doi.org/10.5281/zenodo.23842786","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23842786","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23842785","doi":"https://doi.org/10.5281/zenodo.23842785","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23842785","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W2235627538","https://openalex.org/W7204891229"],"related_works":["https://openalex.org/W7204891229","https://openalex.org/W1997778765","https://openalex.org/W4416085504","https://openalex.org/W6999172178","https://openalex.org/W2302259827","https://openalex.org/W2612002399","https://openalex.org/W7149218528","https://openalex.org/W7149225541","https://openalex.org/W2466492455","https://openalex.org/W2025485890"],"abstract_inverted_index":{"No":[0],"straight-line":[1],"drawing":[2],"of":[3,17,26,35,39],"K14":[4,18],"has":[5],"its":[6],"edges":[7],"split":[8,58],"into":[9],"three":[10],"crossing-free":[11],"layers,":[12],"so":[13],"the":[14,23,33,36],"geometric":[15,37],"thickness":[16,38],"is":[19,48],"4.":[20],"Together":[21],"with":[22,54,77],"upper":[24],"bound":[25,47],"Dillencourt,":[27],"Eppstein":[28],"and":[29,59,70,82],"Hirschberg":[30],"this":[31],"completes":[32],"values":[34],"Kn":[40],"for":[41],"n":[42],"\u2264":[43],"16.":[44],"The":[45],"lower":[46],"a":[49,55,83],"SAT":[50],"computation":[51],"over":[52],"signotopes":[53],"hull-size":[56],"case":[57,80],"an":[60],"Euler-type":[61],"edge":[62],"bound;":[63],"two":[64],"independently":[65],"written":[66],"encoders":[67],"give":[68],"UNSAT,":[69],"every":[71],"leaf":[72],"LRAT":[73],"proof":[74],"was":[75],"checked":[76],"cake_lpr.":[78],"Code,":[79],"trees":[81],"one-command":[84],"checker:":[85],"https://github.com/LeeMarshall1113/ai-math-results":[86],"(results/thickness-k14).":[87]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-11-01T00:00:00"}