Cycle Frames of Complete Multipartite Multigraphs ‐ III |
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| Authors: | A Muthusamy A Shanmuga Vadivu |
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| Affiliation: | Department of Mathematics, Periyar University, Salem, Tamil Nadu, India |
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| 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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| Keywords: | decomposition factorization cycle frame |
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