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On the spouse‐loving variant of the Oberwolfach problem |
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| Authors: | Noah Bolohan Iona Buchanan Andrea Burgess Mateja &#x;ajna Ryan Van Snick |
| Institution: | Noah Bolohan,Iona Buchanan,Andrea Burgess,Mateja ?ajna,Ryan Van Snick |
| Abstract: | We prove that  , 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  if and only if  , except possibly when  is odd and  . In addition, we show that  admits a decomposition into 2‐factors, each a disjoint union of cycles of lengths  , whenever  are all even. |
| Keywords: | 2‐factorization complete graph plus a 1‐factor Oberwolfach problem resolvable minimum covering by cycles spouse‐loving variant |