$\alpha$-Resolvable Cycle Systems for Cycle Length 4
Received:December 05, 2007  Revised:October 07, 2008
Key Words: cycle   cycle system   $\alpha$-resolvable.  
Fund Project:the National Natural Science Foundation of China (No.10971051).
Author NameAffiliation
MA Xiu Wen State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China 
TIAN Zi Hong College of Mathematics and Information Science, Hebei Normal University, Hebei 050016, China 
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Abstract:
      An $m$-cycle system of order $v$ and index $\lambda$, denoted by $m$-${\rm CS}(v,\lambda)$, is a collection of cycles of length $m$ whose edges partition the edges of $\lambda K_{v}$. An $m$-${\rm CS}(v,\lambda)$ is $\alpha$-resolvable if its cycles can be partitioned into classes such that each point of the design occurs in precisely $\alpha$ cycles in each class. The necessary conditions for the existence of such a design are $m|\frac{\lambda v(v-1)}{2},2|\lambda(v-1),m|\alpha v,\alpha|\frac{\lambda(v-1)}{2}$. It is shown in this paper that these conditions are also sufficient when $m=4$.
Citation:
DOI:10.3770/j.issn:1000-341X.2009.06.021
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