{"id":"https://openalex.org/W7214620374","doi":"https://doi.org/10.48550/arxiv.2609.30302","title":"Hull Games of Induced Path Convexities in Graphs","display_name":"Hull Games of Induced Path Convexities in Graphs","publication_year":2026,"publication_date":"2026-09-21","ids":{"openalex":"https://openalex.org/W7214620374","doi":"https://doi.org/10.48550/arxiv.2609.30302"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.30302","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30302","pdf_url":"https://arxiv.org/pdf/2609.30302","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/2609.30302","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153266388","display_name":"Eurinardo Costa","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I243754102","display_name":"Universidade Federal do Cear\u00e1","ror":"https://ror.org/03srtnf24","country_code":"BR","type":"education","lineage":["https://openalex.org/I243754102"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Costa, Eurinardo","raw_affiliation_strings":["Campus Russas , Universidade Federal do Cear\u00e1 , Russas , CE , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Campus Russas , Universidade Federal do Cear\u00e1 , Russas , CE , Brazil","institution_ids":["https://openalex.org/I243754102"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007706893","display_name":"L\u00e9on Almeida","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I243754102","display_name":"Universidade Federal do Cear\u00e1","ror":"https://ror.org/03srtnf24","country_code":"BR","type":"education","lineage":["https://openalex.org/I243754102"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Almeida, Leon","raw_affiliation_strings":["Campus Russas , Universidade Federal do Cear\u00e1 , Russas , CE , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Campus Russas , Universidade Federal do Cear\u00e1 , Russas , CE , Brazil","institution_ids":["https://openalex.org/I243754102"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5135289653","display_name":"Rudini Sampaio","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I243754102","display_name":"Universidade Federal do Cear\u00e1","ror":"https://ror.org/03srtnf24","country_code":"BR","type":"education","lineage":["https://openalex.org/I243754102"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Sampaio, Rudini","raw_affiliation_strings":["Dept. Computa\u00e7\u00e3o , Universidade Federal do Cear\u00e1 , Fortaleza , CE , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. Computa\u00e7\u00e3o , Universidade Federal do Cear\u00e1 , Fortaleza , CE , Brazil","institution_ids":["https://openalex.org/I243754102"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I243754102"],"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9315999746322632,"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":0.9315999746322632,"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":0.05920000001788139,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.0035000001080334187,"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/pspace-completeness","display_name":"PSPACE-completeness","score":0.9160000085830688},{"id":"https://openalex.org/keywords/misere-games","display_name":"mis\u00e8re games","score":0.9470000267028809},{"id":"https://openalex.org/keywords/graph-convexity","display_name":"graph convexity","score":0.6060000061988831},{"id":"https://openalex.org/keywords/geodesic-convexity","display_name":"geodesic convexity","score":0.7590000033378601},{"id":"https://openalex.org/keywords/impartial-games","display_name":"impartial games","score":0.33899998664855957}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.772599995136261},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6912000179290771},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6877999901771545},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6290000081062317},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5246999859809875},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4884999990463257},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.476500004529953},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.4530999958515167},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42809998989105225},{"id":"https://openalex.org/C1465435","wikidata":"https://www.wikidata.org/wiki/Q2916352","display_name":"Longest path problem","level":4,"score":0.4212999939918518},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.41670000553131104},{"id":"https://openalex.org/C127964579","wikidata":"https://www.wikidata.org/wiki/Q649676","display_name":"Alice and Bob","level":3,"score":0.4043000042438507},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.3837999999523163},{"id":"https://openalex.org/C102234262","wikidata":"https://www.wikidata.org/wiki/Q1320931","display_name":"Combinatorial game theory","level":4,"score":0.3752000033855438},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3100999891757965},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.3034999966621399},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.2930999994277954},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.289000004529953},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.2736000120639801},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.273499995470047}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.30302","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30302","pdf_url":"https://arxiv.org/pdf/2609.30302","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.2609.30302","doi":"https://doi.org/10.48550/arxiv.2609.30302","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.30302","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:2609.30302","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30302","pdf_url":"https://arxiv.org/pdf/2609.30302","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":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214620374.pdf","grobid_xml":"https://content.openalex.org/works/W7214620374.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4386857786","https://openalex.org/W4393236678","https://openalex.org/W4409654620","https://openalex.org/W4408128192","https://openalex.org/W4416576155","https://openalex.org/W4410435859","https://openalex.org/W4400938564","https://openalex.org/W4406156200","https://openalex.org/W7163749728","https://openalex.org/W6910411813"],"abstract_inverted_index":{"In":[0,28,51,201],"1984,":[1],"Frank":[2],"Harary":[3],"introduced":[4],"the":[5,16,21,34,64,68,86,111,122,125,152,166,182,210,244,254,269],"first":[6,35],"convexity":[7,23,56],"games":[8,43,57,88,126],"in":[9,101,133,151,165,215,218,227,247],"graphs,":[10],"all":[11],"of":[12,40,78,124,136,187,213,258,283],"them":[13,46],"based":[14,70],"on":[15,38,58,71,75],"geodesic":[17,42],"convexity,":[18],"which":[19],"is":[20,160,250,263,272],"graph":[22,49],"related":[24,252],"to":[25,47,114,120,253,286],"shortest":[26],"paths.":[27],"2024,":[29],"Ara\u00fajo":[30],"et":[31],"al.":[32],"obtained":[33,189],"PSPACE-hardness":[36],"proofs":[37],"some":[39],"these":[41],"and":[44,67,74,91,128,138,156,162,170,217,222,276],"generalized":[45],"any":[48,131],"convexity.":[50],"this":[52,202],"paper,":[53],"we":[54,143,207,239],"investigate":[55],"several":[59],"known":[60],"induced":[61,72,76],"path":[62,153],"convexities:":[63],"monophonic":[65],"$\\mathrm{m}$-convexity":[66],"$\\ell_k$-convexities,":[69],"paths":[73,77,137,248],"size":[79],"at":[80,105],"most":[81,106],"$k$.":[82],"We":[83,108],"prove":[84,144,208],"that":[85,145,209],"hull":[87],"$\\mathrm{CHG}_{\\mathrm{m}}$,":[89],"$\\mathrm{CHG}_{\\ell_k}$":[90,129,150,188,214],"their":[92],"mis\u00e8re":[93],"variants":[94],"are":[95,220],"PSPACE-complete":[96],"for":[97,130,195,242,280],"every":[98],"$k\\ge2$":[99,132,180],"even":[100],"graphs":[102],"with":[103,177,197,205,231],"diameter":[104],"3.":[107],"also":[109],"use":[110],"Sprague-Grundy":[112],"Theory":[113],"obtain":[115],"a":[116],"polynomial":[117],"time":[118],"algorithm":[119],"decide":[121],"winner":[123],"$\\mathrm{CHG}_{\\mathrm{m}}$":[127],"disjoint":[134],"unions":[135],"cycles.":[139],"For":[140,179],"$k\\ge3$":[141],"odd,":[142],"Alice":[146,223,277],"(1st":[147],"player)":[148],"wins":[149,164],"$P_n$":[154,216,228,249],"if":[155,158,169,172,268],"only":[157,171,183,233,279],"$n$":[159,284],"odd":[161],"she":[163],"cycle":[167],"$C_n$":[168,219],"$n=3$":[173],"or":[174,274],"$n=\u03b1\\cdot":[175],"(k+1)-1$":[176],"$\u03b1\\ge2$.":[178],"even,":[181],"periodic":[184,221,273],"nimber":[185,211,270],"sequences":[186,212],"through":[190],"extensive":[191],"computational":[192],"testing":[193],"occurred":[194],"$k=2^h-4$":[196],"$h\\ge3$,":[198],"e.g,":[199],"$k\\in\\{4,12,28,60,\\ldots\\}$.":[200],"case":[203],"($k=2^h-4$":[204],"$h\\ge3$),":[206],"loses":[224,278],"(resp.":[225,229,236],"wins)":[226],"$C_n$)":[230],"$n>k$":[232],"when":[234],"$n=3k+4$":[235],"$n\\in\\{2k+1,5k+3\\}$).":[237],"Finally,":[238],"show":[240],"that,":[241],"$k=2$,":[243],"game":[245,256],"$\\mathrm{CHG}_{\\ell_2}$":[246],"closely":[251],"classical":[255],"\\emph{Couples-are-Forever}":[257],"J.":[259],"H.":[260],"Conway:":[261],"it":[262],"still":[264],"an":[265],"open":[266],"problem":[267],"sequence":[271],"not":[275],"12":[281],"values":[282],"up":[285],"$150$":[287],"million.":[288]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-29T00:00:00"}
