{"id":"https://openalex.org/W7170068879","doi":"https://doi.org/10.48550/arxiv.2607.19134","title":"Parameterized Complexity of Odd Domination and its Generalization","display_name":"Parameterized Complexity of Odd Domination and its Generalization","publication_year":2026,"publication_date":"2026-07-21","ids":{"openalex":"https://openalex.org/W7170068879","doi":"https://doi.org/10.48550/arxiv.2607.19134"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.19134","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.19134","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,"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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2607.19134","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120680851","display_name":"Toranosuke Kokai","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kokai, Toranosuke","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049817236","display_name":"Rin Saito","orcid":"https://orcid.org/0000-0002-3953-4339"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Saito, Rin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5116039201","display_name":"Tatsuhiro Suga","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Suga, Tatsuhiro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5143415698","display_name":"Takahiro Suzuki","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Suzuki, Takahiro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5143456208","display_name":"Yuma Tamura","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tamura, Yuma","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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":0.9876999855041504,"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":0.9876999855041504,"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":0.005799999926239252,"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":0.0010000000474974513,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.9083999991416931},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6162999868392944},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5722000002861023},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5200999975204468},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.48010000586509705},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.475600004196167},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.39079999923706055},{"id":"https://openalex.org/keywords/neighbourhood","display_name":"Neighbourhood (mathematics)","score":0.3294999897480011}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.9083999991416931},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7465999722480774},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7110000252723694},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6162999868392944},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5722000002861023},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5475999712944031},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5200999975204468},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.48010000586509705},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.475600004196167},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.39079999923706055},{"id":"https://openalex.org/C161677786","wikidata":"https://www.wikidata.org/wiki/Q2478475","display_name":"Neighbourhood (mathematics)","level":2,"score":0.3294999897480011},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3188000023365021},{"id":"https://openalex.org/C2777434295","wikidata":"https://www.wikidata.org/wiki/Q959831","display_name":"Girth (graph theory)","level":2,"score":0.29840001463890076},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.288100004196167},{"id":"https://openalex.org/C28723256","wikidata":"https://www.wikidata.org/wiki/Q1400918","display_name":"Feedback vertex set","level":4,"score":0.2750000059604645},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.27480000257492065},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.25040000677108765},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.19134","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.19134","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,"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.19134","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.19134","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,"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":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0,46],"the":[1,14,30,51,55,60,83,86,92,104],"\\textsc{Odd":[2,115],"Domination}":[3],"problem,":[4],"given":[5],"a":[6,10,22,72,112],"graph":[7,99],"$G$":[8,27,37],"and":[9,71,78],"positive":[11],"integer":[12],"$k$,":[13,63],"task":[15],"is":[16,111],"to":[17,82],"determine":[18],"whether":[19],"there":[20],"exists":[21],"vertex":[23,35],"subset":[24],"$D$":[25],"of":[26,33,42,54,85,107,114],"such":[28],"that":[29],"closed":[31],"neighborhood":[32],"each":[34],"in":[36],"contains":[38],"an":[39],"odd":[40],"number":[41],"vertices":[43],"from":[44],"$D$.":[45],"this":[47],"paper,":[48],"we":[49,64,90,102],"investigate":[50,103],"computational":[52],"complexity":[53,106],"problem.":[56],"When":[57],"parameterized":[58,95,105],"by":[59,96],"solution":[61],"size":[62],"establish":[65],"W[1]-hardness":[66,79],"on":[67],"some":[68],"restricted":[69],"graphs":[70],"sharp":[73],"boundary":[74],"between":[75],"fixed-parameter":[76],"tractability":[77],"with":[80],"respect":[81],"girth":[84],"input":[87],"graph.":[88],"Then,":[89],"address":[91],"problem":[93],"when":[94],"several":[97],"structural":[98],"parameters.":[100],"Furthermore,":[101],"\\textsc{Parity":[108],"Domination},":[109],"which":[110],"generalization":[113],"Domination}.":[116]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-23T00:00:00"}