{"id":"https://openalex.org/W4412924930","doi":"https://doi.org/10.1007/s00373-025-02953-2","title":"Cycle Decompositions of Cartesian Products of Two Cycles","display_name":"Cycle Decompositions of Cartesian Products of Two Cycles","publication_year":2025,"publication_date":"2025-07-25","ids":{"openalex":"https://openalex.org/W4412924930","doi":"https://doi.org/10.1007/s00373-025-02953-2"},"language":"en","primary_location":{"id":"doi:10.1007/s00373-025-02953-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-025-02953-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-025-02953-2.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00373-025-02953-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093115667","display_name":"Moriah Aberle","orcid":null},"institutions":[{"id":"https://openalex.org/I117965899","display_name":"University of Hawai\u02bbi at M\u0101noa","ror":"https://ror.org/01wspgy28","country_code":"US","type":"education","lineage":["https://openalex.org/I117965899"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Moriah Aberle","raw_affiliation_strings":["University of Hawai\u2019i at Manoa, Honolulu, USA","University of Hawai'i at Manoa, Honolulu, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Hawai\u2019i at Manoa, Honolulu, USA","institution_ids":["https://openalex.org/I117965899"]},{"raw_affiliation_string":"University of Hawai'i at Manoa, Honolulu, USA","institution_ids":["https://openalex.org/I117965899"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084850534","display_name":"Sarah Gold","orcid":"https://orcid.org/0009-0005-9038-6158"},"institutions":[{"id":"https://openalex.org/I155707491","display_name":"Haverford College","ror":"https://ror.org/04fnrxr62","country_code":"US","type":"education","lineage":["https://openalex.org/I155707491"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sarah Gold","raw_affiliation_strings":["Haverford College, Haverford, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Haverford College, Haverford, USA","institution_ids":["https://openalex.org/I155707491"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093115668","display_name":"Rivkah Moshe","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rivkah Moshe","raw_affiliation_strings":["Boston University, Boston, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Boston University, Boston, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006162887","display_name":"David Offner","orcid":"https://orcid.org/0000-0002-3413-7991"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"David Offner","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, USA"],"raw_orcid":"https://orcid.org/0000-0002-3413-7991","affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5006162887"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16657922,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"41","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9995999932289124,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9894999861717224,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9890000224113464,"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/mathematics","display_name":"Mathematics","score":0.8309431076049805},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.7398976683616638},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6037755608558655},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3424718976020813}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8309431076049805},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.7398976683616638},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6037755608558655},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3424718976020813}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00373-025-02953-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-025-02953-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-025-02953-2.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00373-025-02953-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-025-02953-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-025-02953-2.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310207","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4412924930.pdf"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1972251369","https://openalex.org/W2089852595","https://openalex.org/W2160642345","https://openalex.org/W3134971371","https://openalex.org/W4244686487","https://openalex.org/W4398130993"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2949097972","https://openalex.org/W2141418112","https://openalex.org/W2738565459","https://openalex.org/W3163064202","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W4299640900"],"abstract_inverted_index":{"Abstract":[0],"We":[1,26,57,114],"say":[2],"a":[3,7,13,35,63,72],"graph":[4,8],"H":[5,24],"decomposes":[6,135],"G":[9,19],"if":[10,60,118],"there":[11],"exists":[12],"partition":[14],"of":[15,18,37,49,65,71,85,91,101,111],"the":[16,46,68,98],"edges":[17],"into":[20,82,108],"subgraphs":[21],"isomorphic":[22],"to":[23,28,44],".":[25,56,140],"seek":[27],"characterize":[29],"necessary":[30],"and":[31,75,123,127],"sufficient":[32],"conditions":[33],"for":[34],"cycle":[36,73,78],"length":[38],"k":[39,119,128],",":[40,43,120,122,132],"denoted":[41],"$$C_k$$":[42],"decompose":[45],"Cartesian":[47,69,99],"product":[48,70,100],"two":[50,102,109],"cycles":[51,84,103,110],"$$C_m":[52],"~\\square":[53,137],"~":[54,138],"C_n$$":[55],"prove":[58],"that":[59,97,117],"m":[61,121],"is":[62],"multiple":[64],"3,":[66],"then":[67,133],"$$C_m$$":[74],"any":[76],"other":[77],"can":[79,104],"be":[80,106],"decomposed":[81,107],"3":[83],"equal":[86,112],"length.":[87,113],"This":[88],"extends":[89],"work":[90],"Kotzig,":[92],"who":[93],"proved":[94],"in":[95],"1973":[96],"always":[105],"also":[115],"show":[116],"n":[124],"are":[125],"positive,":[126],"divides":[129],"4":[130],"mn":[131],"$$C_{4k}$$":[134],"$$C_{4m}":[136],"C_{4n}$$":[139]},"counts_by_year":[],"updated_date":"2026-03-11T06:11:40.159057","created_date":"2025-10-10T00:00:00"}