{"id":"https://openalex.org/W4417092735","doi":"https://doi.org/10.1016/j.disc.2026.115198","title":"Between burning and cooling: liminal burning on graphs","display_name":"Between burning and cooling: liminal burning on graphs","publication_year":2026,"publication_date":"2026-05-05","ids":{"openalex":"https://openalex.org/W4417092735","doi":"https://doi.org/10.1016/j.disc.2026.115198"},"language":"en","primary_location":{"id":"doi:10.1016/j.disc.2026.115198","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.disc.2026.115198","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.disc.2026.115198","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082423050","display_name":"Anthony Bonato","orcid":"https://orcid.org/0000-0003-3969-5412"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Anthony Bonato","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037471767","display_name":"Trent G. Marbach","orcid":"https://orcid.org/0000-0002-3708-3095"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Trent G. Marbach","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027143351","display_name":"John Marcoux","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"John Marcoux","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5080247839","display_name":"Teddy Mishura","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Teddy Mishura","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":{"value":3000,"currency":"USD","value_usd":3000},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03135209,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"349","issue":"10","first_page":"115198","last_page":"115198"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.6230000257492065,"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":0.6230000257492065,"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":0.1850000023841858,"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":0.062300000339746475,"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/liminality","display_name":"Liminality","score":0.9847000241279602},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.48539999127388},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.475600004196167},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.45730000734329224},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.45680001378059387}],"concepts":[{"id":"https://openalex.org/C14812997","wikidata":"https://www.wikidata.org/wiki/Q1825499","display_name":"Liminality","level":2,"score":0.9847000241279602},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.48539999127388},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.475600004196167},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47040000557899475},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.45730000734329224},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45680001378059387},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4052000045776367},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.34779998660087585},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3422999978065491},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27399998903274536},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.251800000667572}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1016/j.disc.2026.115198","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.disc.2026.115198","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2505.10727","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.10727","pdf_url":"https://arxiv.org/pdf/2505.10727","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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.2505.10727","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2505.10727","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1016/j.disc.2026.115198","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.disc.2026.115198","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Liminal":[0],"burning":[1,5,68,75,86,98,133,165,170,198],"generalizes":[2],"both":[3],"the":[4,24,28,31,34,44,48,61,66,119,124,161],"and":[6,33,80,107,142,145,166],"cooling":[7,121],"processes":[8],"in":[9,20,193],"graphs.":[10],"In":[11,115],"$k$-liminal":[12,67,97],"burning,":[13,79,190],"a":[14,57,92,171,179,187],"Saboteur":[15],"reveals":[16],"$k$-sets":[17],"of":[18,26,30,46,94,100,113,123,156,163],"vertices":[19],"each":[21],"round,":[22],"with":[23,43,60,105,208],"goal":[25,45],"extending":[27],"length":[29],"game,":[32],"Arsonist":[35],"must":[36],"choose":[37],"sources":[38],"only":[39],"within":[40],"these":[41],"sets,":[42,96],"ending":[47],"game":[49,59],"as":[50,52,139],"soon":[51],"possible.":[53],"The":[54],"result":[55],"is":[56,76,87,173,199,204],"two-player":[58],"corresponding":[62],"optimization":[63],"parameter":[64],"called":[65],"number.":[69],"For":[70],"$k":[71,82],"=":[72,83],"|V(G)|$,":[73],"liminal":[74,85,132,164,169,197],"identical":[77,88],"to":[78,89,127],"for":[81,110,134,175],"1$,":[84],"cooling.":[90],"Using":[91],"variant":[93],"Sperner":[95],"numbers":[99],"hypercubes":[101],"are":[102],"studied":[103],"along":[104],"bounds":[106],"exact":[108,120],"values":[109,112],"various":[111],"$k$.":[114],"particular,":[116],"we":[117],"determine":[118],"number":[122],"$n$-dimensional":[125],"hypercube":[126],"be":[128,151],"$n.$":[129],"We":[130,159,183,206],"analyze":[131],"several":[135,209],"graph":[136,172],"families,":[137],"such":[138],"Cartesian":[140],"grids":[141],"products,":[143],"paths,":[144],"graphs":[146],"whose":[147],"vertex":[148],"sets":[149],"can":[150],"decomposed":[152],"into":[153],"many":[154],"components":[155],"small":[157],"diameter.":[158],"consider":[160],"complexity":[162],"show":[167],"that":[168,191],"PSPACE-complete":[174],"$k\\geq":[176],"2,$":[177],"using":[178],"reduction":[180,188],"from":[181,189],"$3$-QBF.":[182],"also":[184],"prove,":[185],"through":[186],"even":[192],"some":[194],"cases":[195],"when":[196],"likely":[200],"not":[201],"PSPACE-complete,":[202],"it":[203],"co-NP-hard.":[205],"finish":[207],"open":[210],"problems.":[211]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}