Abstract
For two graphs G and H their wreath product has vertex set in which two vertices and are adjacent whenever or and . Clearly, , where is an independent set on n vertices, is isomorphic to the complete m-partite graph in which each partite set has exactly n vertices. A 2-regular subgraph of the complete multipartite graph containing vertices of all but one partite set is called partial 2-factor. For an integer λ, denotes a graph G with uniform edge multiplicity λ. Let J be a set of integers. If can be partitioned into edge-disjoint partial 2-factors consisting cycles of lengths from J, then we say that has a -cycle frame. In this paper, we show that for and , there exists a -cycle frame of if and only if and . In fact our results completely solve the existence of a -cycle frame of .
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