{"id":"https://openalex.org/W7225010748","doi":"https://doi.org/10.5281/zenodo.23838455","title":"A Steiner triple system with a broken chromatic spectrum","display_name":"A Steiner triple system with a broken chromatic spectrum","publication_year":2026,"publication_date":"2026-10-31","ids":{"openalex":"https://openalex.org/W7225010748","doi":"https://doi.org/10.5281/zenodo.23838455"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23838455","doi":"https://doi.org/10.5281/zenodo.23838455","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23838455","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23838455","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159121649","display_name":"P. Graham","orcid":"https://orcid.org/0009-0007-8493-1505","observed_orcids":["https://orcid.org/0009-0007-8493-1505"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Graham, P.","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0007-8493-1505","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5159121649"],"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.8008000254631042,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.8008000254631042,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.13230000436306,"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":0.01730000041425228,"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/steiner-triple-systems","display_name":"Steiner triple systems","score":0.9769999980926514},{"id":"https://openalex.org/keywords/feasible-region","display_name":"feasible region","score":0.6359999775886536},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.5},{"id":"https://openalex.org/keywords/sat-encoding","display_name":"SAT encoding","score":0.47999998927116394},{"id":"https://openalex.org/keywords/drat-trim","display_name":"drat-trim","score":0.8019999861717224},{"id":"https://openalex.org/keywords/unit-propagation","display_name":"unit propagation","score":0.5680000185966492},{"id":"https://openalex.org/keywords/computer-assisted-proof","display_name":"computer-assisted proof","score":0.6830000281333923},{"id":"https://openalex.org/keywords/combinatorial-designs","display_name":"combinatorial designs","score":0.6000000238418579}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7350999712944031},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6944000124931335},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6025999784469604},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5952000021934509},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5547999739646912},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5418000221252441},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5400000214576721},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5074999928474426},{"id":"https://openalex.org/C96865113","wikidata":"https://www.wikidata.org/wiki/Q2946816","display_name":"Certificate","level":2,"score":0.3734000027179718},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.35679998993873596},{"id":"https://openalex.org/C109385661","wikidata":"https://www.wikidata.org/wiki/Q11358307","display_name":"Triple system","level":2,"score":0.34529998898506165},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.34049999713897705},{"id":"https://openalex.org/C2776558979","wikidata":"https://www.wikidata.org/wiki/Q1052","display_name":"Rainbow","level":2,"score":0.3325999975204468},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.30140000581741333},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.29910001158714294},{"id":"https://openalex.org/C175695255","wikidata":"https://www.wikidata.org/wiki/Q4420916","display_name":"Steiner system","level":2,"score":0.290800005197525},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.2775000035762787}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23838455","doi":"https://doi.org/10.5281/zenodo.23838455","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23838455","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23838456","doi":"https://doi.org/10.5281/zenodo.23838456","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23838456","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23838455","doi":"https://doi.org/10.5281/zenodo.23838455","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23838455","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":null,"license_id":null,"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":6,"referenced_works":["https://openalex.org/W118367033","https://openalex.org/W134339645","https://openalex.org/W2066859294","https://openalex.org/W2152553909","https://openalex.org/W4400973078","https://openalex.org/W7116674059"],"related_works":["https://openalex.org/W7096902749","https://openalex.org/W2152553909","https://openalex.org/W2747641264","https://openalex.org/W7098304108","https://openalex.org/W2962680068","https://openalex.org/W1802287274","https://openalex.org/W2055414226","https://openalex.org/W1998949919","https://openalex.org/W2587289525","https://openalex.org/W2399542500"],"abstract_inverted_index":{"A":[0],"bicoloring":[1,34,164],"of":[2,22,28,48,86,99,127,129,146,154,161,174],"a":[3,84,95,162,169,175,183],"Steiner":[4,51,96],"triple":[5,52,97],"system":[6,24,53,85,98],"colors":[7,111],"its":[8,138],"points":[9],"so":[10,117],"that":[11,44,102,125],"every":[12,49],"block":[13],"receives":[14],"exactly":[15,36,106,109,115],"two":[16,148],"colors,":[17,137],"and":[18,58,67,79,108,157,181,204,214],"the":[19,23,26,45,61,70,118,147,152,198,201,205,218,232],"feasible":[20,46,90,139],"set":[21,27,47,91,140],"is":[25,120,141,165],"integers":[29],"$k$":[30,37],"for":[31],"which":[32],"some":[33],"uses":[35],"colors.":[38],"Mario":[39],"Gionfriddo":[40,68],"conjectured":[41],"in":[42,65,72],"2003":[43],"bicolorable":[50],"has":[54,89,103,189],"no":[55],"gaps;":[56],"Tuza":[57],"Voloshin":[59,80],"listed":[60],"question":[62],"as":[63],"open":[64,82],"2008,":[66],"restated":[69],"conjecture":[71,119],"2025.":[73],"In":[74],"2014":[75],"Gionfriddo,":[76],"Guardo,":[77],"Milazzo":[78],"left":[81],"whether":[83],"order":[87,100,130],"39":[88,101,131],"$\\{3,5\\}$.":[92,142],"We":[93],"give":[94],"bicolorings":[104,126,149],"with":[105,114],"three":[107],"five":[110,136],"but":[112],"none":[113],"four,":[116],"false.":[121],"With":[122],"their":[123],"theorem":[124],"systems":[128],"use":[132],"three,":[133],"four":[134],"or":[135],"The":[143,159,196],"class":[144],"sizes":[145],"come":[150],"from":[151],"tables":[153],"Colbourn,":[155],"Dinitz":[156],"Rosa.":[158],"absence":[160],"four-color":[163],"proved":[166],"by":[167,179,182,194,209,225,228],"computer:":[168],"SAT":[170],"solver's":[171],"clausal":[172],"refutation":[173],"direct":[176],"encoding,":[177],"checked":[178],"DRAT-trim":[180],"separate":[184],"unit-propagation":[185],"checker.":[186],"This":[187],"work":[188],"not":[190,222],"yet":[191,223],"been":[192],"reviewed":[193,224],"experts.":[195,226],"proofs,":[197],"search":[199],"code,":[200],"certificate":[202],"checkers":[203],"text":[206],"were":[207],"produced":[208],"AI":[210,229],"models":[211,230],"(from":[212],"OpenAI":[213],"Anthropic),":[215],"working":[216],"under":[217,231],"author's":[219,233],"direction.":[220,234],"Computer-assisted;":[221],"Produced":[227]},"counts_by_year":[],"updated_date":"2026-11-02T09:45:03.842371","created_date":"2026-11-01T00:00:00"}
