Sparseness of 4-cycle systems
Sparseness of 4-cycle systems
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发表时间：
2012-09
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通讯作者：
Yuichiro Fujiwara;S. Wu;H. Fu
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作者：
Yuichiro Fujiwara;S. Wu;H. Fu
通过推广Steiner三元系上Erd\H{o}s'r-稀疏猜想中的稀疏性概念，研究了四圈系统的位形回避问题.一个v阶的4-圈系统4CS（v）称为r-稀疏的，如果对于每个满足1 1的整数j和足够大的整数v，存在一个常数c，使得存在一个v阶的严格r-稀疏的4-圈填充，其中有cv^2个4-圈。
An avoidance problem of configurations in 4-cycle systems is investigated by generalizing the notion of sparseness, which is originally from Erd\H{o}s' r-sparse conjecture on Steiner triple systems. A 4-cycle system of order v, 4CS(v), is said to be r-sparse if for every integer j satisfying 1 1 and sufficiently large integer v there exists a constant number c such that there exists a strictly r-sparse 4-cycle packing of order v with cv^2 4-cycles.