{"id":"https://openalex.org/W7143510698","doi":"https://doi.org/10.48550/arxiv.2603.26006","title":"Computing fixed point free automorphisms of graphs","display_name":"Computing fixed point free automorphisms of graphs","publication_year":2026,"publication_date":"2026-03-27","ids":{"openalex":"https://openalex.org/W7143510698","doi":"https://doi.org/10.48550/arxiv.2603.26006"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.26006","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.26006","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.26006","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5130979978","display_name":"Aida Abiad","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Abiad, Aida","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130936306","display_name":"Gabriel Coutinho","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Coutinho, Gabriel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130980555","display_name":"Emanuel Juliano","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Juliano, Emanuel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101510751","display_name":"Vin\u00edcius F. dos Santos","orcid":"https://orcid.org/0000-0002-4608-4559"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Santos, Vinicius F. dos","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5089306974","display_name":"Sjanne Zeijlemaker","orcid":"https://orcid.org/0000-0002-6121-7698"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zeijlemaker, Sjanne","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.8949000239372253,"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":0.8949000239372253,"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":0.02539999969303608,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.024900000542402267,"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/automorphism","display_name":"Automorphism","score":0.7843999862670898},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5885999798774719},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.5009999871253967},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4426000118255615},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.43950000405311584},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4088999927043915},{"id":"https://openalex.org/keywords/induced-subgraph","display_name":"Induced subgraph","score":0.3433000147342682},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.33469998836517334}],"concepts":[{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.7843999862670898},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7501000165939331},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6402999758720398},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5885999798774719},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.545199990272522},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.5009999871253967},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4426000118255615},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.43950000405311584},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4088999927043915},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.3433000147342682},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.33469998836517334},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.32670000195503235},{"id":"https://openalex.org/C115988155","wikidata":"https://www.wikidata.org/wiki/Q3262192","display_name":"Decision problem","level":2,"score":0.32440000772476196},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.32409998774528503},{"id":"https://openalex.org/C6049932","wikidata":"https://www.wikidata.org/wiki/Q834981","display_name":"Graph automorphism","level":5,"score":0.31690001487731934},{"id":"https://openalex.org/C187407849","wikidata":"https://www.wikidata.org/wiki/Q6889712","display_name":"Modular decomposition","level":5,"score":0.31139999628067017},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.3073999881744385},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.30320000648498535},{"id":"https://openalex.org/C59824394","wikidata":"https://www.wikidata.org/wiki/Q5141281","display_name":"Cograph","level":5,"score":0.29170000553131104},{"id":"https://openalex.org/C191241153","wikidata":"https://www.wikidata.org/wiki/Q6027240","display_name":"Induced subgraph isomorphism problem","level":5,"score":0.25679999589920044},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.2524000108242035},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.25209999084472656}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.26006","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.26006","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:10.48550/arxiv.2603.26006","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.26006","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":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"1981,":[1],"Lubiw":[2],"proved":[3],"that":[4,24,38],"the":[5,66,92,111],"fixed":[6],"point":[7],"free":[8],"automorphism":[9,23],"problem":[10,35,112],"(FPFAut)":[11],"is":[12,53],"NP-complete:":[13],"given":[14],"a":[15,73,100,104],"graph":[16],"G,":[17],"determine":[18],"whether":[19],"there":[20],"exists":[21],"an":[22,55],"maps":[25],"no":[26],"vertex":[27],"of":[28,58,62,69,80,97,106,113],"G":[29],"to":[30,44],"itself.":[31],"We":[32,71],"revisit":[33],"this":[34],"and":[36,48,86],"prove":[37],"FPFAut":[39],"remains":[40],"NP-complete":[41],"when":[42],"restricted":[43],"split,":[45],"bipartite,":[46],"k-subdivided,":[47],"H-free":[49],"graphs,":[50,84],"if":[51],"H":[52],"not":[54],"induced":[56],"subgraph":[57],"P_4.":[59],"The":[60],"class":[61],"P_4-free":[63],"graphs":[64],"receives":[65],"special":[67],"name":[68],"cographs.":[70],"provide":[72],"polynomial":[74],"time":[75],"algorithm":[76],"for":[77],"three":[78],"extensions":[79],"cographs:":[81],"bounded":[82],"modular-width":[83],"tree-cographs":[85],"P_4-sparse":[87],"graphs.":[88,98],"Our":[89],"approach":[90],"uses":[91],"well":[93],"known":[94],"modular":[95],"decomposition":[96],"As":[99],"consequence,":[101],"we":[102],"generalize":[103],"result":[105],"Abiad":[107],"et.":[108],"al.":[109],"on":[110],"computing":[114],"2-homogeneous":[115],"equitable":[116],"partitions.":[117]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-31T00:00:00"}