Cycle decompositions of the line graph of \(K_ n\)
A 4-cycle system of a graph \(G\) is a set of 4-cycles that induces a partition of the edge set of \(G\). This note supplements a result of K. Heinrich and G. M. Nonay about a certain set of 4-cycles of \(K_ n\). The proof of the result used a 4-cycle system of the line graph of \(K_ n\). Here the following theorem is proved: If \(n\equiv 1\pmod 8\), then there exists a 4-cycle system of the line graph of \(K_ n\).
scientific article; zbMATH DE number 165757