On the spouse‐loving variant of the Oberwolfach problem. Issue 4 (6th January 2019)

• Record Type: Journal Article
• Authors: Bolohan, Noah; Buchanan, Iona; Burgess, Andrea; Šajna, Mateja; Van Snick, Ryan
• Is Part Of: Journal of combinatorial designs. Volume 27:Issue 4(2019:Apr.)
• Page Start: 251
• Page End: 260
• Publication Date: 2019-01-06
• Subjects: 2‐factorization -- complete graph plus a 1‐factor -- Oberwolfach problem -- resolvable minimum covering by cycles -- spouse‐loving variant; Combinatorial designs and configurations -- Periodicals; Configurations et schémas combinatoires -- Périodiques; 511.6
• DOI: 10.1002/jcd.21645
• Languages: English
• ISSNs: 1063-8539

Abstract

Abstract: We prove that K n + I, the complete graph of even order with a 1‐factor duplicated, admits a decomposition into 2‐factors, each a disjoint union of cycles of length m ≥ 5 if and only if m ∣ n, except possibly when m is odd and n = 4 m . In addition, we show that K n + I admits a decomposition into 2‐factors, each a disjoint union of cycles of lengths m 1, …, m t, whenever m 1, …, m t are all even.