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Using the technique of amalgamation‐detachment, we show that the complete equipartite multigraph    λ   K   n  ×  mcan be decomposed into cycles of lengthsc  1   m  ,  ⋯  ,   c  k   m    (plus a 1‐factor if the degree is odd) whenever there exists a decomposition of    λ  m   K  ninto cycles of lengthsc  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.

Decomposing Complete Equipartite Multigraphs into Cycles of Variable Lengths: The Amalgamation‐detachment Approach