{"id":"https://openalex.org/W4387723926","doi":"https://doi.org/10.48550/arxiv.2310.09678","title":"Tree Containment Above Minimum Degree is FPT","display_name":"Tree Containment Above Minimum Degree is FPT","publication_year":2023,"publication_date":"2023-10-14","ids":{"openalex":"https://openalex.org/W4387723926","doi":"https://doi.org/10.48550/arxiv.2310.09678"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2310.09678","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2310.09678","pdf_url":"https://arxiv.org/pdf/2310.09678","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2310.09678","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075328697","display_name":"Fedor V. Fomin","orcid":"https://orcid.org/0000-0003-1955-4612"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Fomin, Fedor V.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051709720","display_name":"Petr A. Golovach","orcid":"https://orcid.org/0000-0002-2619-2990"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Golovach, Petr A.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021164153","display_name":"Danil Sagunov","orcid":"https://orcid.org/0000-0003-3327-9768"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sagunov, Danil","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5102983476","display_name":"Kirill Simonov","orcid":"https://orcid.org/0000-0001-9436-7310"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Simonov, Kirill","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5075328697"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.998199999332428,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.998199999332428,"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/T10374","display_name":"Advanced Graph Theory Research","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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.982200026512146,"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/combinatorics","display_name":"Combinatorics","score":0.8682448863983154},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.7030344009399414},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6823606491088867},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5716997981071472},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.5597589612007141},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5291013717651367},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5017991065979004},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4685707092285156},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.4416779577732086},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1046762764453888}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8682448863983154},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.7030344009399414},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6823606491088867},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5716997981071472},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.5597589612007141},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5291013717651367},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5017991065979004},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4685707092285156},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.4416779577732086},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1046762764453888},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2310.09678","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2310.09678","pdf_url":"https://arxiv.org/pdf/2310.09678","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2310.09678","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2310.09678","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":"pmh:oai:arXiv.org:2310.09678","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2310.09678","pdf_url":"https://arxiv.org/pdf/2310.09678","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320323299","display_name":"Norges Forskningsr\u00e5d","ror":"https://ror.org/00epmv149"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4387723926.pdf","grobid_xml":"https://content.openalex.org/works/W4387723926.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2051058708","https://openalex.org/W1494268238","https://openalex.org/W154868527","https://openalex.org/W1983207144","https://openalex.org/W4313216298","https://openalex.org/W2071797893","https://openalex.org/W3002741190","https://openalex.org/W3037640829","https://openalex.org/W2893201198","https://openalex.org/W2884117239"],"abstract_inverted_index":{"According":[0],"to":[1,54],"the":[2,24],"classic":[3],"Chv{\u00e1}tal's":[4],"Lemma":[5],"from":[6],"1977,":[7],"a":[8,39,51],"graph":[9,34,83],"of":[10,28,67,72],"minimum":[11],"degree":[12],"$\u03b4(G)$":[13],"contains":[14,50],"every":[15],"tree":[16,40],"on":[17,42,78],"$\u03b4(G)+1$":[18],"vertices.":[19],"Our":[20],"main":[21,74],"result":[22,75],"is":[23,76],"following":[25],"algorithmic":[26],"\"extension\"":[27],"Chv\u00e1tal's":[29],"Lemma:":[30],"For":[31],"any":[32],"$n$-vertex":[33],"$G$,":[35],"integer":[36],"$k$,":[37],"and":[38,85],"$T$":[41],"at":[43],"most":[44],"$\u03b4(G)+k$":[45],"vertices,":[46],"deciding":[47],"whether":[48],"$G$":[49],"subgraph":[52],"isomorphic":[53],"$T$,":[55],"can":[56],"be":[57],"done":[58],"in":[59],"time":[60],"$f(k)\\cdot":[61],"n^{\\mathcal{O}(1)}$":[62],"for":[63],"some":[64],"function":[65],"$f$":[66],"$k$":[68],"only.":[69],"The":[70],"proof":[71],"our":[73],"based":[77],"an":[79],"interplay":[80],"between":[81],"extremal":[82],"theory":[84],"parameterized":[86],"algorithms.":[87]},"counts_by_year":[],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
