{"id":"https://openalex.org/W7133201672","doi":"https://doi.org/10.48550/arxiv.2602.23825","title":"Local Equivalence Classes of Distance-Hereditary Graphs using Split Decompositions","display_name":"Local Equivalence Classes of Distance-Hereditary Graphs using Split Decompositions","publication_year":2026,"publication_date":"2026-02-27","ids":{"openalex":"https://openalex.org/W7133201672","doi":"https://doi.org/10.48550/arxiv.2602.23825"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.23825","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5127871297","display_name":"Nicholas Connolly","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Connolly, Nicholas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101660591","display_name":"S. Nishio","orcid":"https://orcid.org/0000-0003-2659-5930"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nishio, Shin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5081979382","display_name":"Kae Nemoto","orcid":"https://orcid.org/0000-0003-3938-0808"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nemoto, Kae","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5127871297"],"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":0.3671000003814697,"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":0.3671000003814697,"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/T10849","display_name":"Finite Group Theory Research","score":0.23569999635219574,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.12210000306367874,"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/equivalence-relation","display_name":"Equivalence relation","score":0.5914000272750854},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5848000049591064},{"id":"https://openalex.org/keywords/multipartite","display_name":"Multipartite","score":0.5295000076293945},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5162000060081482},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.4535999894142151},{"id":"https://openalex.org/keywords/equivalence-class","display_name":"Equivalence class (music)","score":0.4406000077724457},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4293999969959259}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7250000238418579},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6478999853134155},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.5914000272750854},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5848000049591064},{"id":"https://openalex.org/C166733315","wikidata":"https://www.wikidata.org/wiki/Q6934831","display_name":"Multipartite","level":4,"score":0.5295000076293945},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5162000060081482},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4629000127315521},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.4535999894142151},{"id":"https://openalex.org/C2777044963","wikidata":"https://www.wikidata.org/wiki/Q5384707","display_name":"Equivalence class (music)","level":2,"score":0.4406000077724457},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4293999969959259},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.41909998655319214},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.37459999322891235},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.3059999942779541},{"id":"https://openalex.org/C125080357","wikidata":"https://www.wikidata.org/wiki/Q45715","display_name":"Complete graph","level":3,"score":0.2761000096797943},{"id":"https://openalex.org/C38754835","wikidata":"https://www.wikidata.org/wiki/Q2003238","display_name":"Strongly connected component","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.23825","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.23825","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.23825","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.23825","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":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":{"Local":[0],"complement":[1],"is":[2,36],"a":[3,14,37,88,110],"graph":[4],"operation":[5,21],"formalized":[6],"by":[7,66],"Bouchet":[8,42],"which":[9],"replaces":[10],"the":[11,29,32,114],"neighborhood":[12],"of":[13,31,74,113],"chosen":[15],"vertex":[16],"with":[17],"its":[18],"edge-complement.":[19],"This":[20],"induces":[22],"an":[23],"equivalence":[24,34,99],"relation":[25],"on":[26,98],"graphs;":[27],"determining":[28],"size":[30],"resulting":[33],"classes":[35],"challenging":[38],"problem":[39],"in":[40],"general.":[41],"obtained":[43],"formulas":[44,69],"only":[45],"for":[46,70],"paths":[47],"and":[48,50,82,102],"cycles,":[49],"brute-force":[51],"methods":[52],"are":[53,107],"limited":[54],"to":[55,94,119],"very":[56],"small":[57],"graphs.":[58,84],"In":[59],"this":[60],"work,":[61],"we":[62,103],"extend":[63],"these":[64,105],"results":[65],"deriving":[67],"explicit":[68],"several":[71],"broad":[72],"families":[73],"distance-hereditary":[75],"graphs,":[76,80],"including":[77],"complete":[78],"multipartite":[79],"clique-stars,":[81],"repeater":[83],"Our":[85],"approach":[86],"uses":[87],"technique":[89],"known":[90],"as":[91],"split":[92],"decomposition":[93],"establish":[95],"upper":[96],"bounds":[97,106],"class":[100],"sizes,":[101],"prove":[104],"tight":[108],"through":[109],"combinatorial":[111],"enumeration":[112],"graphs'":[115],"decomposed":[116],"structure":[117],"up":[118],"symmetry.":[120]},"counts_by_year":[],"updated_date":"2026-05-03T08:25:01.440150","created_date":"2026-03-03T00:00:00"}
