{"id":"https://openalex.org/W4412050731","doi":"https://doi.org/10.46298/fi.12478","title":"Constructing disjoint Steiner trees in Sierpi\u0144ski graphs","display_name":"Constructing disjoint Steiner trees in Sierpi\u0144ski graphs","publication_year":2025,"publication_date":"2025-07-05","ids":{"openalex":"https://openalex.org/W4412050731","doi":"https://doi.org/10.46298/fi.12478"},"language":"en","primary_location":{"id":"doi:10.46298/fi.12478","is_oa":true,"landing_page_url":"https://doi.org/10.46298/fi.12478","pdf_url":"https://fi.episciences.org/16000/pdf","source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://fi.episciences.org/16000/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034004918","display_name":"Chenxu Yang","orcid":"https://orcid.org/0000-0003-2523-7090"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chenxu Yang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100435510","display_name":"Ping Li","orcid":"https://orcid.org/0000-0002-3518-4802"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ping Li","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-3518-4802","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103286474","display_name":"Yaping Mao","orcid":"https://orcid.org/0000-0001-9134-237X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yaping Mao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069246449","display_name":"Eddie Cheng","orcid":"https://orcid.org/0000-0003-4526-7983"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eddie Cheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5112786437","display_name":"Ralf Klasing","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ralf Klasing","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":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16555519,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"Volume 194, Issue 1","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9383999705314636,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9383999705314636,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9366999864578247,"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/steiner-tree-problem","display_name":"Steiner tree problem","score":0.755057692527771},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7084645628929138},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6368680000305176},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5657744407653809},{"id":"https://openalex.org/keywords/sierpinski-triangle","display_name":"Sierpinski triangle","score":0.5397776961326599},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4179023802280426},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34084656834602356},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.0829077959060669}],"concepts":[{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.755057692527771},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7084645628929138},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6368680000305176},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5657744407653809},{"id":"https://openalex.org/C27176706","wikidata":"https://www.wikidata.org/wiki/Q663365","display_name":"Sierpinski triangle","level":3,"score":0.5397776961326599},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4179023802280426},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34084656834602356},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.0829077959060669},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.46298/fi.12478","is_oa":true,"landing_page_url":"https://doi.org/10.46298/fi.12478","pdf_url":"https://fi.episciences.org/16000/pdf","source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-05352292v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05352292","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Fundamenta Informaticae, 2025, Volume194,Issue1, ⟨10.46298/fi.12478⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.46298/fi.12478","is_oa":true,"landing_page_url":"https://doi.org/10.46298/fi.12478","pdf_url":"https://fi.episciences.org/16000/pdf","source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3764912099","display_name":null,"funder_award_id":"12201375","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5329913919","display_name":null,"funder_award_id":"2017-ZJ-Y21","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6297067728","display_name":"\u62c9\u59c6\u9f50\u7406\u8bba\u548c\u52a0\u83b1-\u62c9\u59c6\u9f50\u6570\u53ca\u5176\u5e94\u7528\u7814\u7a76","funder_award_id":"12061059","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8902729962","display_name":null,"funder_award_id":"12471329","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4412050731.pdf","grobid_xml":"https://content.openalex.org/works/W4412050731.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W6600103761","https://openalex.org/W6600882715"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1991823548","https://openalex.org/W2118320476","https://openalex.org/W2161182859","https://openalex.org/W2025658531","https://openalex.org/W1503036335","https://openalex.org/W4244816249","https://openalex.org/W2115973883","https://openalex.org/W3187836939","https://openalex.org/W3196396437"],"abstract_inverted_index":{"Let":[0],"$G$":[1,19,129],"be":[2,154],"a":[3,81,218],"graph":[4,82],"and":[5,35,136,148,150,152,197],"$S\\subseteq":[6],"V(G)$":[7],"with":[8,214],"$|S|\\geq":[9],"2$.":[10],"Then":[11],"the":[12,56,64,98,112,144,188,198,211,232],"trees":[13,118],"$T_1,":[14],"T_2,":[15],"\\cdots,":[16],"T_\\ell$":[17],"in":[18,121,164],"are":[20,70,141,174],"\\emph{internally":[21],"disjoint":[22,103],"Steiner":[23,72,117,239],"trees}":[24],"connecting":[25,119],"$S$":[26,120],"(or":[27],"$S$-Steiner":[28,104],"trees)":[29],"if":[30,52],"$E(T_i)":[31,58],"\\cap":[32,59],"E(T_j":[33,60],")=\\emptyset$":[34,61],"$V(T_i)\\cap":[36,66],"V(T_j)=S$":[37],"for":[38,177,193,203],"every":[39],"pair":[40],"of":[41,80,101,115,128,143,146,158,160,181,191,201,236],"distinct":[42],"integers":[43],"$i,j$,":[44],"$1":[45],"\\leq":[46,49],"i,":[47],"j":[48],"\\ell$.":[50],"Similarly,":[51],"we":[53,186],"only":[54],"have":[55],"condition":[57,65],"but":[62],"without":[63],"V(T_j)=S$,":[67],"then":[68],"they":[69,151],"\\emph{edge-disjoint":[71],"trees}.":[73],"The":[74,106,123],"\\emph{generalized":[75,107],"$k$-connectivity},":[76],"denoted":[77],"by":[78],"$\u03ba_k(G)$,":[79],"$G$,":[83],"is":[84,97,111,130,210],"defined":[85,131],"as":[86,132,156],"$\u03ba_k(G)=\\min\\{\u03ba_G(S)|S":[87],"\\subseteq":[88],"V(G)":[89,134],"\\":[90,92,135,137],"\\textrm{and}":[91],"|S|=k":[93],"\\}$,":[94],"where":[95,207],"$\u03ba_G(S)$":[96],"maximum":[99,113],"number":[100,114],"internally":[102],"trees.":[105],"local":[108],"edge-connectivity}":[109],"$\u03bb_{G}(S)$":[110],"edge-disjoint":[116],"$G$.":[122],"{\\it":[124],"generalized":[125,170],"$k$-edge-connectivity}":[126],"$\u03bb_k(G)$":[127],"$\u03bb_k(G)=\\min\\{\u03bb_{G}(S)\\,|\\,S\\subseteq":[133],"|S|=k\\}$.":[138],"These":[139],"measures":[140,157],"generalizations":[142],"concepts":[145],"connectivity":[147],"edge-connectivity,":[149],"can":[153],"used":[155],"vulnerability":[159],"networks.":[161],"It":[162],"is,":[163],"general,":[165],"difficult":[166],"to":[167],"compute":[168],"these":[169,221],"connectivities.":[171],"However,":[172],"there":[173],"precise":[175],"results":[176],"some":[178,233],"special":[179],"classes":[180],"graphs.":[182,238],"In":[183],"this":[184],"paper,":[185],"obtain":[187],"exact":[189,199],"value":[190,200],"$\u03bb_{k}(S(n,\\ell))$":[192],"$3\\leq":[194,204],"k\\leq":[195,205],"\\ell^n$,":[196],"$\u03ba_{k}(S(n,\\ell))$":[202],"\\ell$,":[206],"$S(n,":[208],"\\ell)$":[209],"Sierpi\u0144ski":[212,237,243],"graphs":[213,222],"order":[215],"$\\ell^n$.":[216],"As":[217],"direct":[219],"consequence,":[220],"provide":[223],"additional":[224],"interesting":[225],"examples":[226],"when":[227],"$\u03bb_{k}(S(n,\\ell))=\u03ba_{k}(S(n,\\ell))$.":[228],"We":[229],"also":[230],"study":[231],"network":[234],"properties":[235],"Tree;":[240],"Generalized":[241],"Connectivity;":[242],"Graph":[244]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}