{"id":"https://openalex.org/W2036302144","doi":"https://doi.org/10.1080/019697298125623","title":"UNCOLORABLE TRIVALENT GRAPHS","display_name":"UNCOLORABLE TRIVALENT GRAPHS","publication_year":1998,"publication_date":"1998-06-01","ids":{"openalex":"https://openalex.org/W2036302144","doi":"https://doi.org/10.1080/019697298125623","mag":"2036302144"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1080/019697298125623","pdf_url":null,"source":{"id":"https://openalex.org/S117436046","display_name":"Cybernetics & Systems","issn_l":"0196-9722","issn":["0196-9722","1087-6553"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064825165","display_name":"GEORGE SPENCER-BROWN","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"GEORGE SPENCER-BROWN","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5064825165"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":0,"max":55},"biblio":{"volume":"29","issue":"4","first_page":"319","last_page":"344"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9763,"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":0.9763,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.965,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T12288","display_name":"Optimization and Search Problems","score":0.9252,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/linkage","display_name":"Linkage (software)","score":0.43807375}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.80558795},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.55173504},{"id":"https://openalex.org/C2779182362","wikidata":"https://www.wikidata.org/wiki/Q17126187","display_name":"Session (web analytics)","level":2,"score":0.5085672},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.46835676},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.44374847},{"id":"https://openalex.org/C31266012","wikidata":"https://www.wikidata.org/wiki/Q6554340","display_name":"Linkage (software)","level":3,"score":0.43807375},{"id":"https://openalex.org/C2776445246","wikidata":"https://www.wikidata.org/wiki/Q1792644","display_name":"Style (visual arts)","level":2,"score":0.43228292},{"id":"https://openalex.org/C554936623","wikidata":"https://www.wikidata.org/wiki/Q199657","display_name":"Reading (process)","level":2,"score":0.4284826},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33154064},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32699555},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31283358},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1968354},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.16974252},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.124788076},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.11609864},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07910946},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.07864988},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.07382631},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1080/019697298125623","pdf_url":null,"source":{"id":"https://openalex.org/S117436046","display_name":"Cybernetics & Systems","issn_l":"0196-9722","issn":["0196-9722","1087-6553"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.58}],"grants":[],"datasets":[],"versions":[],"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W621808327","https://openalex.org/W4387820098","https://openalex.org/W4296749040","https://openalex.org/W4230197055","https://openalex.org/W3196207352","https://openalex.org/W3084261076","https://openalex.org/W2951724202","https://openalex.org/W2808944898","https://openalex.org/W2576399385","https://openalex.org/W1996614773"],"abstract_inverted_index":{"The":[0,81,116,147,181],"text":[1],"that":[2,88,97,101,120,141,166,190],"follows":[3],"is":[4,123],"an":[5],"extended":[6],"write-up":[7],"of":[8,14,28,41,49,57,84,128,133,150,213],"the":[9,15,29,39,54,58,93,110,121,151,164,185,200,204,208],"Ross":[10],"Ashby":[11],"Memorial":[12],"Lecture":[13],"International":[16],"Federation":[17],"for":[18,125],"Systems":[19,36],"Research,":[20],"delivered":[21],"by":[22,114],"invitation":[23],"to":[24,77,207],"a":[25,75,131,169],"plenary":[26],"session":[27],"Thirteenth":[30],"European":[31],"Meeting":[32],"on":[33,43,158,163],"Cybernetics":[34],"and":[35,65,70,96,198],"Research":[37],"at":[38],"University":[40],"Vienna":[42],"April":[44],"10,":[45],"1996.":[46],"For":[47],"ease":[48],"reading":[50],"I":[51],"have":[52],"retained":[53],"informal":[55],"style":[56],"lecture":[59],"theater,":[60],"but":[61,162],"without":[62],"sacrificing":[63],"accuracy":[64],"rigor":[66],"in":[67,91,154,203,210],"my":[68],"theorems":[69],"proofs.":[71],"Isaacs":[72,142,186],"1975":[73],"detailed":[74],"way":[76,95,156],"make":[78],"uncolorable":[79,145],"3-graphs.":[80,146],"first":[82,205],"part":[83,118,183,206],"this":[85,159],"communication":[86],"shows":[87,119],"it":[89],"is,":[90],"principle,":[92],"only":[94],"all":[98,144],"such":[99],"graphs":[100],"can":[102],"define":[103],"maps":[104],"must":[105],"be":[106,179],"nonplanar,":[107],"thus":[108],"proving":[109,140],"four-color":[111],"map":[112,152],"theorem":[113,153],"exclusion.":[115],"second":[117],"method":[122],"ineffectual":[124],"closed":[126],"chains":[127,167],"units":[129],"with":[130,168],"linkage":[132],"less":[134],"or":[135,171,176],"more":[136,196],"than":[137],"3,":[138],"so":[139],"found":[143],"associated":[148],"proof":[149,202],"no":[155,195],"depends":[157],"stronger":[160],"result":[161],"fact":[165],"triple":[170],"greater":[172],"linkage,":[173],"whether":[174],"colorable":[175],"not,":[177],"cannot":[178],"planar.":[180],"third":[182],"simplifies":[184],"dot":[187],"product,":[188],"proves":[189],"his":[191],"Q":[192],"class":[193],"has":[194],"members,":[197],"relates":[199],"4-color":[201],"proofs":[209],"Appendix":[211],"5":[212],"Spencer-Brown":[214],"1997.":[215]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2036302144","counts_by_year":[],"updated_date":"2025-01-17T08:21:33.074030","created_date":"2016-06-24"}