The metamorphosis of lambda-fold 4-wheel systems into lambda-fold 4-cycle systems (Q2725026)

A \(\lambda\)-fold 4-wheel system of order \(n\) is a decomposition of the complete multigraph \(\lambda K_n\) into 4-wheels. If after deleting from every 4-wheel the central vertex and the four edges incident with it (so that only the 4-cycle rim is retained) one can reassemble the deleted edges into 4-cycles then one has the metamorphosis, as in the title of the article. The authors determine (apart from 5 possible exceptional orders) necessary and sufficient conditions for the existence of a \(\lambda\)-fold 4-wheel system of order \(n\) which can be transformed into a \(\lambda\)-fold 4-cycle system of order \(n\).