α-可分解的8长圈的存在性

摘要

In this paper, we discussed the existence ofα-resolvable cycle systems for cycle length 8 by using direct and recursive construction methods. It is shown that the conditions for existence ofα-resolvable 8 -CS(υ,λ) are both necessary and sufficient except for the few case whenυ≡4, 6, 12, 14, 15( mod 16) andυ = 34 .%研究α-可分解的圈长为8的圈系统的存在性问题。通过直接构造和递归构造相结合的方法,证明了α-可分解的8-CS(υ,λ)存在的必要条件也是充分的,除去υ≡4,6,12,14,15(mod 16)及v=34的可能情形外。