{"id":"https://openalex.org/W4400512506","doi":"https://doi.org/10.61091/ars159-14","title":"5-Regular Subgraphs in Hypercubes","display_name":"5-Regular Subgraphs in Hypercubes","publication_year":2024,"publication_date":"2024-06-30","ids":{"openalex":"https://openalex.org/W4400512506","doi":"https://doi.org/10.61091/ars159-14"},"language":"en","primary_location":{"id":"doi:10.61091/ars159-14","is_oa":true,"landing_page_url":"http://dx.doi.org/10.61091/ars159-14","pdf_url":"https://combinatorialpress.com/article/ars/5-regular-subgraphs-in-hypercubes.pdf","source":{"id":"https://openalex.org/S73158690","display_name":"Ars Combinatoria","issn_l":"0381-7032","issn":["0381-7032","2817-5204"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4323439501","host_organization_name":"Charles Babbage Research Centre","host_organization_lineage":["https://openalex.org/P4323439501"],"host_organization_lineage_names":["Charles Babbage Research Centre"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ars Combinatoria","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://combinatorialpress.com/article/ars/5-regular-subgraphs-in-hypercubes.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056769658","display_name":"Y. M. Borse","orcid":"https://orcid.org/0000-0003-2606-7919"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Y. M. Borse","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108626737","display_name":"S. R. Shaikh","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. R. Shaikh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5046598141","display_name":"J. B. Saraf","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. B. Saraf","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":0.10340808,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"159","issue":"1","first_page":"165","last_page":"178"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.988099992275238,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9599000215530396,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8756853342056274},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.8712315559387207},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8643882870674133},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.7146748900413513},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6036221981048584},{"id":"https://openalex.org/keywords/induced-subgraph","display_name":"Induced subgraph","score":0.5135229229927063},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36731529235839844},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2769728899002075}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8756853342056274},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.8712315559387207},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8643882870674133},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.7146748900413513},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6036221981048584},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.5135229229927063},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36731529235839844},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2769728899002075},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.61091/ars159-14","is_oa":true,"landing_page_url":"http://dx.doi.org/10.61091/ars159-14","pdf_url":"https://combinatorialpress.com/article/ars/5-regular-subgraphs-in-hypercubes.pdf","source":{"id":"https://openalex.org/S73158690","display_name":"Ars Combinatoria","issn_l":"0381-7032","issn":["0381-7032","2817-5204"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4323439501","host_organization_name":"Charles Babbage Research Centre","host_organization_lineage":["https://openalex.org/P4323439501"],"host_organization_lineage_names":["Charles Babbage Research Centre"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ars Combinatoria","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.61091/ars159-14","is_oa":true,"landing_page_url":"http://dx.doi.org/10.61091/ars159-14","pdf_url":"https://combinatorialpress.com/article/ars/5-regular-subgraphs-in-hypercubes.pdf","source":{"id":"https://openalex.org/S73158690","display_name":"Ars Combinatoria","issn_l":"0381-7032","issn":["0381-7032","2817-5204"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4323439501","host_organization_name":"Charles Babbage Research Centre","host_organization_lineage":["https://openalex.org/P4323439501"],"host_organization_lineage_names":["Charles Babbage Research Centre"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ars Combinatoria","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1320946443","display_name":null,"funder_award_id":"MTR/2018/000447","funder_id":"https://openalex.org/F4320334771","funder_display_name":"Science and Engineering Research Board"}],"funders":[{"id":"https://openalex.org/F4320320719","display_name":"Department of Science and Technology, Ministry of Science and Technology, India","ror":"https://ror.org/0101xrq71"},{"id":"https://openalex.org/F4320334771","display_name":"Science and Engineering Research Board","ror":"https://ror.org/03ffdsr55"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400512506.pdf","grobid_xml":"https://content.openalex.org/works/W4400512506.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2916710807","https://openalex.org/W2413588304","https://openalex.org/W2774705104","https://openalex.org/W2013252038","https://openalex.org/W2386598361","https://openalex.org/W1519742024","https://openalex.org/W2078375028","https://openalex.org/W2105222637","https://openalex.org/W2032950096"],"abstract_inverted_index":{"One":[0],"of":[1,5,23,48,85,193],"the":[2,6,45,121],"fundamental":[3],"properties":[4],"hypercube":[7],"\\(":[8,17,25,32,36,56,60,70,78,81,86,92,105,111,124,132,137,142,149,158,165,173,182,189,194,198,207],"Q_n":[9,18,87,133,195],"\\)":[10,19,27,34,58,72,88,109,134,144,163,167,196,203,213],"is":[11,14,90,102,147,168],"that":[12,89,131,146,187],"it":[13],"bipancyclic":[15,153],"as":[16],"has":[20,197],"a":[21,53,136],"cycle":[22],"length":[24],"l":[26,33,39,71,79,143,159,166,176],"for":[28,73,104,123],"every":[29,188],"even":[30,170],"integer":[31,55,171],"with":[35,59],"4":[37,114],"\\leq":[38,40,62,64,175,177],"2^n":[41,178],"\\).":[42,115,128,179],"We":[43,129],"consider":[44],"following":[46],"problem":[47,101,122],"generalizing":[49],"this":[50,100,117],"property:":[51],"For":[52,180],"given":[54],"k":[57,63,82,93,106,112,125,183,190],"3":[61,108],"n":[65],"\\),":[66,184],"determine":[67],"all":[68],"integers":[69],"which":[74],"there":[75],"exists":[76],"an":[77,169],"\\)-vertex,":[80],"\\)-regular":[83,139,191],"subgraph":[84,140,192],"both":[91,148],"\\)-connected":[94,151],"and":[95,110,152,155],"bipancyclic.":[96],"The":[97],"solution":[98],"to":[99],"known":[103],"=":[107,113,126],"In":[116],"paper,":[118],"we":[119,185],"solve":[120],"5":[127,138,150],"prove":[130],"contains":[135],"on":[141],"vertices":[145],"if":[154,157],"only":[156],"\\in":[160],"\\{32,":[161],"48\\}":[162],"or":[164,204],"satisfying":[172],"52":[174],"general":[181],"establish":[186],"2^k,":[199],"2^k":[200,208],"+":[201,209,211],"2^{k-1}":[202,210],"at":[205],"least":[206],"2^{k-3}":[212],"vertices.":[214]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}