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\(1\)-factorizations of Cayley graphs. (English) Zbl 1208.20027

Summary: We prove that all connected Cayley graphs of every finite group \(Q\times H\) are \(1\)-factorizable, where \(Q\) is any non-trivial group of \(2\)-power order and \(H\) is any group of odd order.

MSC:

20D60 Arithmetic and combinatorial problems involving abstract finite groups
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
20F05 Generators, relations, and presentations of groups
20D15 Finite nilpotent groups, \(p\)-groups
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