{"id":"https://openalex.org/W4387402806","doi":"https://doi.org/10.37236/11113","title":"Improved Pyrotechnics: Closer to the Burning Number Conjecture","display_name":"Improved Pyrotechnics: Closer to the Burning Number Conjecture","publication_year":2023,"publication_date":"2023-10-06","ids":{"openalex":"https://openalex.org/W4387402806","doi":"https://doi.org/10.37236/11113"},"language":"en","primary_location":{"id":"doi:10.37236/11113","is_oa":true,"landing_page_url":"https://doi.org/10.37236/11113","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i4p2/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i4p2/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103233969","display_name":"Paul Bastide","orcid":"https://orcid.org/0000-0002-4041-6903"},"institutions":[{"id":"https://openalex.org/I4210146044","display_name":"\u00c9cole Normale Sup\u00e9rieure de Rennes","ror":"https://ror.org/03rxtdc22","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210146044","https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Paul Bastide","raw_affiliation_strings":["ENS Rennes - LaBri"],"affiliations":[{"raw_affiliation_string":"ENS Rennes - LaBri","institution_ids":["https://openalex.org/I4210146044"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029166445","display_name":"Marthe Bonamy","orcid":"https://orcid.org/0000-0001-7905-8018"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]},{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Marthe Bonamy","raw_affiliation_strings":["CNRS, LaBRI, Universit\u00e9 de Bordeaux"],"affiliations":[{"raw_affiliation_string":"CNRS, LaBRI, Universit\u00e9 de Bordeaux","institution_ids":["https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210160189","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082423050","display_name":"Anthony Bonato","orcid":"https://orcid.org/0000-0003-3969-5412"},"institutions":[{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Anthony Bonato","raw_affiliation_strings":["Ryerson University, Toronto"],"affiliations":[{"raw_affiliation_string":"Ryerson University, Toronto","institution_ids":["https://openalex.org/I530967"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015923364","display_name":"Pierre Charbit","orcid":"https://orcid.org/0000-0001-9401-040X"},"institutions":[{"id":"https://openalex.org/I4210117673","display_name":"Institut de Recherche en Informatique Fondamentale","ror":"https://ror.org/02krdtz55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210089394","https://openalex.org/I4210117673","https://openalex.org/I4210139971"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre Charbit","raw_affiliation_strings":["IRIF, Paris"],"affiliations":[{"raw_affiliation_string":"IRIF, Paris","institution_ids":["https://openalex.org/I4210117673"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000112998","display_name":"Shahin Kamali","orcid":"https://orcid.org/0000-0003-1404-2212"},"institutions":[{"id":"https://openalex.org/I46247651","display_name":"University of Manitoba","ror":"https://ror.org/02gfys938","country_code":"CA","type":"education","lineage":["https://openalex.org/I46247651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Shahin Kamali","raw_affiliation_strings":["University of Manitoba, Winnipeg"],"affiliations":[{"raw_affiliation_string":"University of Manitoba, Winnipeg","institution_ids":["https://openalex.org/I46247651"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089101660","display_name":"Th\u00e9o Pierron","orcid":"https://orcid.org/0000-0002-5586-5613"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I4210155607","display_name":"Laboratoire d'Informatique en Images et Syst\u00e8mes d'Information","ror":"https://ror.org/04dv4he91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I188626449","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210155607","https://openalex.org/I48430043"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Th\u00e9o Pierron","raw_affiliation_strings":["LIRIS, Universit\u00e9 de Lyon, Lyon"],"affiliations":[{"raw_affiliation_string":"LIRIS, Universit\u00e9 de Lyon, Lyon","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I4210155607"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038963808","display_name":"Mika\u00ebl Rabie","orcid":"https://orcid.org/0000-0001-6782-7625"},"institutions":[{"id":"https://openalex.org/I4210117673","display_name":"Institut de Recherche en Informatique Fondamentale","ror":"https://ror.org/02krdtz55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210089394","https://openalex.org/I4210117673","https://openalex.org/I4210139971"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mika\u00ebl Rabie","raw_affiliation_strings":["IRIF, Paris"],"affiliations":[{"raw_affiliation_string":"IRIF, Paris","institution_ids":["https://openalex.org/I4210117673"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5103233969"],"corresponding_institution_ids":["https://openalex.org/I4210146044"],"apc_list":null,"apc_paid":null,"fwci":0.8387,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.71098379,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"30","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9524000287055969,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9524000287055969,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8577326536178589},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7852505445480347},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7041335105895996},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5523480176925659},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5407521724700928},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5194603800773621},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.49552762508392334},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4906531870365143},{"id":"https://openalex.org/keywords/vertex-connectivity","display_name":"Vertex connectivity","score":0.46794596314430237},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4126189351081848},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40674877166748047},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07852402329444885}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8577326536178589},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7852505445480347},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7041335105895996},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5523480176925659},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5407521724700928},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5194603800773621},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.49552762508392334},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4906531870365143},{"id":"https://openalex.org/C2983226441","wikidata":"https://www.wikidata.org/wiki/Q3115621","display_name":"Vertex connectivity","level":4,"score":0.46794596314430237},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4126189351081848},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40674877166748047},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07852402329444885},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/11113","is_oa":true,"landing_page_url":"https://doi.org/10.37236/11113","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i4p2/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04587525v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04587525","pdf_url":"https://hal.science/hal-04587525/document","source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The Electronic Journal of Combinatorics, 2023, 30 (4), &#x27E8;10.37236/11113&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.37236/11113","is_oa":true,"landing_page_url":"https://doi.org/10.37236/11113","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i4p2/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4387402806.pdf"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W198180607","https://openalex.org/W2011105641","https://openalex.org/W2064084823","https://openalex.org/W2741500259","https://openalex.org/W2962945827","https://openalex.org/W2963174930","https://openalex.org/W2972087955","https://openalex.org/W2996203613","https://openalex.org/W3016925894","https://openalex.org/W3141776272","https://openalex.org/W4285034613"],"related_works":["https://openalex.org/W1980648360","https://openalex.org/W2023302035","https://openalex.org/W2339534957","https://openalex.org/W2988282395","https://openalex.org/W341486533","https://openalex.org/W2557579792","https://openalex.org/W2353691047","https://openalex.org/W4313216298","https://openalex.org/W2090952304","https://openalex.org/W2750508132"],"abstract_inverted_index":{"The":[0,144],"Burning":[1],"Number":[2],"Conjecture":[3],"claims":[4],"that":[5,30,64,117],"for":[6,67,122,133,149],"every":[7],"connected":[8,90],"graph":[9,40,91],"$G$":[10,92],"of":[11,38,52,69,77,88,93],"order":[12,37,94],"$n,$":[13,95],"its":[14,45],"burning":[15,86],"number":[16,76,87],"satisfies":[17],"$b(G)":[18,98],"\\le":[19,99],"\\lceil":[20],"\\sqrt{n}\\,":[21],"\\rceil.$":[22],"While":[23],"the":[24,36,39,49,60,65,81,85,105,111,118],"conjecture":[25,66,119],"remains":[26],"open,":[27],"we":[28,115],"prove":[29,63],"it":[31],"is":[32,41,48],"asymptotically":[33],"true":[34],"when":[35],"much":[42],"larger":[43],"than":[44],"growth,":[46],"which":[47],"maximal":[50],"distance":[51],"a":[53,56,74,89],"vertex":[54],"to":[55,73],"well-chosen":[57],"path":[58],"in":[59],"graph.":[61],"We":[62,79],"graphs":[68,124,137,150],"bounded":[70],"growth":[71],"reduces":[72],"finite":[75],"cases.":[78],"provide":[80],"best-known":[82,146],"bound":[83],"on":[84,104],"given":[96],"by":[97],"\\sqrt{4n/3}":[100],"+":[101],"1,$":[102],"improving":[103],"previously":[106],"known":[107],"$\\sqrt{3n/2}+O(1)$":[108],"bound.":[109],"Using":[110],"improved":[112],"upper":[113],"bound,":[114],"show":[116],"almost":[120],"holds":[121,132],"all":[123,134],"with":[125,138,151],"minimum":[126,139,152],"degree":[127,140,153],"at":[128,141],"least":[129,142],"$3$":[130],"and":[131],"large":[135],"enough":[136],"$4$.":[143],"previous":[145],"result":[147],"was":[148],"$23$.":[154]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-11T14:59:36.786465","created_date":"2025-10-10T00:00:00"}
