$\alpha$-Resolvable Cycle Systems for Cycle Length 4 |
Received:December 05, 2007 Revised:October 07, 2008 |
Key Words:
cycle cycle system $\alpha$-resolvable.
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Fund Project:the National Natural Science Foundation of China (No.10971051). |
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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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