Decomposition of \(K_{m,n}\) into short cycles
It is shown that if \(m\), \(n\) are even integers, \(m\geq 4\), \(n\geq 6\), then the complete bipartite graph \(K_{m,n}\) can be decomposed into \(p\) copies of \(C_4\), \(q\) copies of \(C_6\) and \(r\) copies of \(C_8\) (where \(C_i\) is the cycle of length \(i\)) whenever \(4p+ 6q+ 8r= m\cdot n\). A similar result is obtained for \(K_{m,n}-F\) (\(F\) a 1-factor) when \(n\) is odd.
scientific article; zbMATH DE number 1322012