{"id":"https://openalex.org/W4388001245","doi":"https://doi.org/10.1007/s00453-023-01181-5","title":"Token Sliding on Graphs of Girth Five","display_name":"Token Sliding on Graphs of Girth Five","publication_year":2023,"publication_date":"2023-10-28","ids":{"openalex":"https://openalex.org/W4388001245","doi":"https://doi.org/10.1007/s00453-023-01181-5"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-023-01181-5","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00453-023-01181-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-023-01181-5.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00453-023-01181-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108137936","display_name":"Valentin Bartier","orcid":null},"institutions":[{"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"]},{"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/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"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Valentin Bartier","raw_affiliation_strings":["CNRS, LIRIS, Universit\u00e9 de Lyon, Universit\u00e9 Claude Bernard Lyon 1, Villeurbanne, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS, LIRIS, Universit\u00e9 de Lyon, Universit\u00e9 Claude Bernard Lyon 1, Villeurbanne, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I4210155607"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044190443","display_name":"Nicol\u00e1s Bousquet","orcid":"https://orcid.org/0000-0003-0170-0503"},"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/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"]},{"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"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nicolas Bousquet","raw_affiliation_strings":["CNRS, LIRIS, Universit\u00e9 de Lyon, Universit\u00e9 Claude Bernard Lyon 1, Villeurbanne, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS, LIRIS, Universit\u00e9 de Lyon, Universit\u00e9 Claude Bernard Lyon 1, Villeurbanne, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I4210155607"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012314738","display_name":"Jihad Hanna","orcid":null},"institutions":[{"id":"https://openalex.org/I98635879","display_name":"American University of Beirut","ror":"https://ror.org/04pznsd21","country_code":"LB","type":"education","lineage":["https://openalex.org/I98635879"]}],"countries":["LB"],"is_corresponding":false,"raw_author_name":"Jihad Hanna","raw_affiliation_strings":["Department of Computer Science, American University of Beirut, Beirut, Lebanon"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, American University of Beirut, Beirut, Lebanon","institution_ids":["https://openalex.org/I98635879"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051065386","display_name":"Amer E. Mouawad","orcid":"https://orcid.org/0000-0003-2481-4968"},"institutions":[{"id":"https://openalex.org/I180437899","display_name":"University of Bremen","ror":"https://ror.org/04ers2y35","country_code":"DE","type":"education","lineage":["https://openalex.org/I180437899"]},{"id":"https://openalex.org/I98635879","display_name":"American University of Beirut","ror":"https://ror.org/04pznsd21","country_code":"LB","type":"education","lineage":["https://openalex.org/I98635879"]}],"countries":["DE","LB"],"is_corresponding":false,"raw_author_name":"Amer E. Mouawad","raw_affiliation_strings":["Department of Computer Science, American University of Beirut, Beirut, Lebanon","Fachbereich 3 - Mathematik und Informatik, University of Bremen, Bremen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, American University of Beirut, Beirut, Lebanon","institution_ids":["https://openalex.org/I98635879"]},{"raw_affiliation_string":"Fachbereich 3 - Mathematik und Informatik, University of Bremen, Bremen, Germany","institution_ids":["https://openalex.org/I180437899"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073548944","display_name":"Sebastian Siebertz","orcid":"https://orcid.org/0000-0002-6347-1198"},"institutions":[{"id":"https://openalex.org/I180437899","display_name":"University of Bremen","ror":"https://ror.org/04ers2y35","country_code":"DE","type":"education","lineage":["https://openalex.org/I180437899"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sebastian Siebertz","raw_affiliation_strings":["Fachbereich 3 - Mathematik und Informatik, University of Bremen, Bremen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich 3 - Mathematik und Informatik, University of Bremen, Bremen, Germany","institution_ids":["https://openalex.org/I180437899"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5108137936"],"corresponding_institution_ids":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I4210155607"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.1918,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.56814319,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"86","issue":"2","first_page":"638","last_page":"655"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9979000091552734,"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/T11567","display_name":"semigroups and automata theory","score":0.9979000091552734,"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/algorithm","display_name":"Algorithm","score":0.5471899509429932},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3412216305732727},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3275139331817627}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5471899509429932},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3412216305732727},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3275139331817627}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00453-023-01181-5","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00453-023-01181-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-023-01181-5.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03829759v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03829759","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"WG, Jun 2022, Tubingen, Germany. pp.56--69, &#x27E8;10.1007/s00453-023-01181-5&#x27E9;","raw_type":"Conference papers"}],"best_oa_location":{"id":"doi:10.1007/s00453-023-01181-5","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00453-023-01181-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-023-01181-5.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1199503345","display_name":null,"funder_award_id":"ANR-18-CE40-0032","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6876561401","display_name":null,"funder_award_id":"ANR-18","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320324729","display_name":"Universit\u00e4t Bremen","ror":"https://ror.org/04ers2y35"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4388001245.pdf"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W318401295","https://openalex.org/W1495095571","https://openalex.org/W1842542859","https://openalex.org/W1883335082","https://openalex.org/W1970459509","https://openalex.org/W1976090101","https://openalex.org/W1997048861","https://openalex.org/W2036722182","https://openalex.org/W2110762325","https://openalex.org/W2129794490","https://openalex.org/W2145799305","https://openalex.org/W2294088579","https://openalex.org/W2321811561","https://openalex.org/W2345745843","https://openalex.org/W2610183793","https://openalex.org/W2754517646","https://openalex.org/W2757068865","https://openalex.org/W2795775903","https://openalex.org/W2899024477","https://openalex.org/W2962848607","https://openalex.org/W2963967898","https://openalex.org/W2963968150","https://openalex.org/W2964148273","https://openalex.org/W2964160217","https://openalex.org/W3010964268","https://openalex.org/W3117234799","https://openalex.org/W3214844150","https://openalex.org/W4297404807","https://openalex.org/W6929077377"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2530322880"],"abstract_inverted_index":{"Abstract":[0],"In":[1,285],"the":[2,120,231,234,237,291,312,324,327,348,369,388,395,401,404],"Token":[3,295,391],"Sliding":[4,296,392],"problem":[5,238,313,349,370],"we":[6,219,271,288],"are":[7,272],"given":[8],"a":[9,57,225,243,279,282,333,384],"graph":[10],"G":[11,34],"and":[12,24,173,323,366],"two":[13],"independent":[14,91,132,222,246],"sets":[15,92,247],"$$I_s$$":[16,250],"<mml:math":[17,26,40,67,104,123,141,159,184,251,260,338],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[18,27,41,68,105,124,142,160,185,252,261,339],"<mml:msub>":[19,28,71,76,83,125,144,149,162,167,187,192,253,262],"<mml:mi>I</mml:mi>":[20,29,72,77,84,126,145,150,163,168,188,193,254,263],"<mml:mi>s</mml:mi>":[21,151,255],"</mml:msub>":[22,31,74,79,86,128,147,152,165,170,190,199,256,265],"</mml:math>":[23,32,47,89,119,129,154,172,216,257,266,345],"$$I_t$$":[25,259],"<mml:mi>t</mml:mi>":[30,169,264],"in":[33],"of":[35,90,134,227,233,245,294,318,329,355,377,387,390,397,403],"size":[36,135],"$$k":[37],"\\ge":[38,336],"1$$":[39],"<mml:mrow>":[42,69,106,143,161,186,194,201,210,340],"<mml:mi>k</mml:mi>":[43],"<mml:mo>\u2265</mml:mo>":[44,342],"<mml:mn>1</mml:mn>":[45,73,110,116,146,197],"</mml:mrow>":[46,88,118,153,171,198,207,214,215,344],".":[48,217,300,360],"The":[49],"goal":[50],"is":[51,130,314,371],"to":[52,274,281],"decide":[53],"whether":[54,240,330],"there":[55,241,331],"exists":[56,242,332],"sequence":[58,244],"$$\\langle":[59],"I_1,":[60],"I_2,":[61],"\\ldots":[62],",":[63,100,137,155],"I_\\ell":[64],"\\rangle":[65],"$$":[66],"<mml:mo>\u27e8</mml:mo>":[70],"<mml:mo>,</mml:mo>":[75,80,82,111,113,204],"<mml:mn>2</mml:mn>":[78],"<mml:mo>\u2026</mml:mo>":[81,112],"<mml:mi>\u2113</mml:mi>":[85,114,164],"<mml:mo>\u27e9</mml:mo>":[87],"such":[93,346],"that":[94,248,347,368],"for":[95],"all":[96],"$$j":[97],"\\in":[98,182],"\\{1,\\ldots":[99],"\\ell":[101],"-":[102],"1\\}$$":[103],"<mml:mi>j</mml:mi>":[107,127,189,195],"<mml:mo>\u2208</mml:mo>":[108,208],"<mml:mo>{</mml:mo>":[109,202],"<mml:mo>-</mml:mo>":[115],"<mml:mo>}</mml:mo>":[117,206],"set":[121,133,223],"$$I_j$$":[122],"an":[131],"k":[136,299],"$$I_1":[138],"=":[139,157,179],"I_s$$":[140],"<mml:mo>=</mml:mo>":[148,166,200],"$$I_\\ell":[156],"I_t$$":[158],"$$I_j":[174],"\\triangle":[175],"I_{j":[176],"+":[177],"1}":[178],"\\{u,":[180],"v\\}":[181],"E(G)$$":[183],"<mml:mi>\u25b5</mml:mi>":[191],"<mml:mo>+</mml:mo>":[196],"<mml:mi>u</mml:mi>":[203],"<mml:mi>v</mml:mi>":[205],"<mml:mi>E</mml:mi>":[209],"<mml:mo>(</mml:mo>":[211],"<mml:mi>G</mml:mi>":[212],"<mml:mo>)</mml:mo>":[213],"Intuitively,":[218],"view":[220],"each":[221,269],"as":[224],"collection":[226],"tokens":[228,398],"placed":[229],"on":[230,290,316,353,375,400],"vertices":[232],"graph.":[235,406],"Then,":[236],"asks":[239],"transforms":[249],"into":[258],"where":[267],"at":[268,357],"step":[270],"allowed":[273],"slide":[275],"one":[276],"token":[277],"from":[278],"vertex":[280],"neighboring":[283],"vertex.":[284],"this":[286],"paper,":[287],"focus":[289],"parameterized":[292,297,393],"complexity":[293],"by":[298,303,394],"As":[301],"shown":[302],"Bartier":[304],"et":[305],"al.":[306],"(Algorithmica":[307],"83(9):2914\u20132951,":[308],"2021.":[309],"https://doi.org/10.1007/s00453-021-00848-1":[310],"),":[311],"-hard":[315],"graphs":[317,354,376],"girth":[319,356,378,402],"four":[320],"or":[321,380],"less,":[322],"authors":[325],"posed":[326],"question":[328,364],"constant":[334],"$$p":[335],"5$$":[337],"<mml:mi>p</mml:mi>":[341],"<mml:mn>5</mml:mn>":[343],"becomes":[350],"fixed-parameter":[351,373],"tractable":[352,374],"least":[358],"p":[359],"We":[361],"answer":[362],"their":[363],"positively":[365],"prove":[367],"indeed":[372],"five":[379],"more,":[381],"which":[382],"establishes":[383],"full":[385],"classification":[386],"tractability":[389],"number":[396],"based":[399],"input":[405]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-05-13T08:25:38.343686","created_date":"2025-10-10T00:00:00"}