{"id":"https://openalex.org/W7220739317","doi":"https://doi.org/10.48550/arxiv.2610.04124","title":"An upper bound on the proper hat guessing number of graphs","display_name":"An upper bound on the proper hat guessing number of graphs","publication_year":2026,"publication_date":"2026-10-02","ids":{"openalex":"https://openalex.org/W7220739317","doi":"https://doi.org/10.48550/arxiv.2610.04124"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.04124","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04124","pdf_url":"https://arxiv.org/pdf/2610.04124","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.04124","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139456229","display_name":"Ioannis Kakatelis","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Kakatelis, Ioannis","raw_affiliation_strings":["Czech Technical University , Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Czech Technical University , Czech Republic","institution_ids":["https://openalex.org/I44504214"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5139456229"],"corresponding_institution_ids":["https://openalex.org/I44504214"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9125999808311462,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9125999808311462,"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":0.07010000199079514,"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":0.003100000089034438,"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/graph-coloring","display_name":"graph coloring","score":0.5260000228881836},{"id":"https://openalex.org/keywords/upper-bounds","display_name":"upper bounds","score":0.7590000033378601},{"id":"https://openalex.org/keywords/maximum-degree","display_name":"maximum degree","score":0.8849999904632568},{"id":"https://openalex.org/keywords/binomial-random-graphs","display_name":"binomial random graphs","score":0.8240000009536743},{"id":"https://openalex.org/keywords/winning-strategies","display_name":"winning strategies","score":0.6000000238418579},{"id":"https://openalex.org/keywords/graph-games","display_name":"graph games","score":0.33899998664855957}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8165000081062317},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7638999819755554},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6589000225067139},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6000000238418579},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4936000108718872},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49059998989105225},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4779999852180481},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4629000127315521},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.43869999051094055},{"id":"https://openalex.org/C2781315470","wikidata":"https://www.wikidata.org/wiki/Q193623","display_name":"Binomial (polynomial)","level":2,"score":0.4156000018119812},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3481000065803528},{"id":"https://openalex.org/C34718186","wikidata":"https://www.wikidata.org/wiki/Q209875","display_name":"Binomial coefficient","level":2,"score":0.3303000032901764},{"id":"https://openalex.org/C41054675","wikidata":"https://www.wikidata.org/wiki/Q185547","display_name":"Binomial distribution","level":2,"score":0.2824000120162964},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.2734000086784363},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.26010000705718994},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.25}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.04124","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04124","pdf_url":"https://arxiv.org/pdf/2610.04124","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},{"id":"doi:10.48550/arxiv.2610.04124","doi":"https://doi.org/10.48550/arxiv.2610.04124","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.04124","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"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":"pmh:oai:arXiv.org:2610.04124","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04124","pdf_url":"https://arxiv.org/pdf/2610.04124","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321005","display_name":"Ministerstvo \u0160kolstv\u00ed, Ml\u00e1de\u017ee a T\u011blov\u00fdchovy","ror":"https://ror.org/037n8p820"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220739317.pdf","grobid_xml":"https://content.openalex.org/works/W7220739317.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7167888474","https://openalex.org/W4319793558","https://openalex.org/W7134046615","https://openalex.org/W3195953319","https://openalex.org/W2906251963","https://openalex.org/W7171720239","https://openalex.org/W4220794129","https://openalex.org/W4381737079","https://openalex.org/W4389121045","https://openalex.org/W2943840525"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,23,28,45,60,74,97,105,113,122,131,139,145,150,162,168],"proper":[3,18,50,98,163],"hat":[4,61,99,164],"guessing":[5,16,100,165],"game":[6],"on":[7,27,138],"graphs,":[8],"introduced":[9],"by":[10,121,176],"Adriaensen":[11],"et":[12,126],"al.":[13,127],"in":[14,149],"Hat":[15],"with":[17],"colorings.":[19],"In":[20],"this":[21,94],"game,":[22],"players":[24,81,114],"are":[25],"seated":[26],"vertices":[29,142],"of":[30,40,54,63,76,108,124,141,167,187],"a":[31,38,49,71,117],"graph":[32,171],"$G$":[33],"and":[34,144],"assigned":[35],"hats":[36],"from":[37],"set":[39],"$k$":[41],"colors":[42,62,109],"such":[43,111],"that":[44,103,112,135,161,185],"resulting":[46],"assignment":[47],"forms":[48],"coloring.":[51],"The":[52,80],"visibility":[53],"each":[55],"vertex":[56],"is":[57,88,96,104,173],"limited":[58],"to":[59,93,159],"their":[64,77],"neighborhood.":[65],"Then":[66],"they":[67],"must":[68],"simultaneously":[69],"output":[70],"guess":[72,87],"about":[73],"color":[75],"own":[78],"hat.":[79],"win":[82],"if":[83],"at":[84],"least":[85],"one":[86],"correct.":[89],"A":[90],"parameter":[91],"related":[92],"problem":[95],"number":[101,107,140,166],"$\\operatorname{HG}_{P}(G)$":[102],"maximum":[106,146,188],"$m$":[110],"can":[115],"guarantee":[116],"winning":[118],"strategy.":[119],"Motivated":[120],"work":[123],"Shurman":[125],"\\cite{shurman2026upper},":[128],"we":[129,183],"establish":[130],"first":[132],"upper":[133],"bound":[134],"depends":[136],"both":[137],"$n$":[143],"degree":[147,189],"$\u0394$":[148],"case":[151],"where":[152,178],"$\u0394\\geq":[153],"\\frac{n}{e+1}$.":[154],"This":[155],"result":[156],"leads":[157],"us":[158],"show":[160],"binomial":[169],"random":[170],"$G_{n,1/2}$":[172],"bounded":[174],"above":[175],"$cn$,":[177],"$c":[179],"\\approx":[180],"1.366$.":[181],"Finally,":[182],"prove":[184],"graphs":[186],"$(1-\u03b3)n$":[190],"for":[191],"some":[192],"fixed":[193],"$\u03b3\\in":[194],"(0,1]$":[195],"cannot":[196],"have":[197],"$\\operatorname{HG}_{P}(G)":[198],"=":[199],"(2-o(1))n$.":[200]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-07T00:00:00"}
