Decomposing complete equipartite multigraphs into cycles of variable lengths: the amalgamation-detachment approach

09/20/2019

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by   Amin Bahmanian, et al.

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Using the technique of amalgamation-detachment, we show that the complete equipartite multigraph λ K_n× m can be decomposed into cycles of lengths c_1m,...,c_km (plus a 1-factor if the degree is odd) whenever there exists a decomposition of λ m K_n into cycles of lengths c_1, ...,c_k (plus a 1-factor if the degree is odd). In addition, we give sufficient conditions for the existence of some other, related cycle decompositions of the complete equipartite multigraph λ K_n× m.