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| Solutions to six classes of the Oberwolfach problem OP$(4^{a},s^b)$ |
| LI Xiao-fang1, CAO Hai-tao?2 |
1. Department of Common Course, Anhui Xinhua University, Hefei 230088, China
2. Institute of Mathematics, Nanjing Normal University, Nanjing 210023, China |
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Abstract The problem of determining whether $K_n$ (for $n$ odd) or $K_n$ minus a 1-factor (for $n$ even) has a 2-factorization is called Oberwolfach problem. The notation OP$(m_1^{\alpha_1},m_2^{\alpha_2},\cdots,m_t^{\alpha_t})$ represents the case in which each 2-factor consists of exactly $\alpha_i$ cycles of length $m_i$ for $i=1,2,\cdots,t$. Proved that the OP$(4^{a},s^b)$ with $a\geq 0$, $b=2,3$, $s=3,5,6$ and $(a,s,b)\not=(0,3,2)$ have solutions.
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Received: 16 January 2014
Published: 10 June 2018
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六类Oberwolfach问题OP$(4^{a},s^b)$的解
完全图$K_n$($n$为奇数)或$K_n-I$($n$为偶数, $I$为$K_n$的1-因子)是否有2-因子分解称为Oberwolfach问题. 每个2-因子恰包含$\alpha_i$个长为$m_i$的圈($i=1,2,\cdots,t$)的Oberwolfach问题记为OP$(m_1^{\alpha_1},m_2^{\alpha_2},\cdots,m_t^{\alpha_t})$. 证明了对任意的$a\ge 0$, $b=2,3$和$s=3,5,6$, 且$(a,s,b)\not=(0,3,2)$, 都存在OP$(4^{a},s^b)$的解.
关键词：
Oberwolfach问题,
圈可分组设计,
圈支架
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