Orthogonal \([k-1,k+1]\)-factorizations in graphs
Let \(G\) be a graph. Let \(F= \{F_1, F_2,\dots, F_d\}\) be a factorization of \(G\), and let \(H\) be a subgraph of \(G\). If \(H\) has exactly one edge in common with \(F_i\) for all \(i= 1,2,\dots, d\), then we say that \(F\) is orthogonal to \(H\). This paper proves that for any \(d\)-matching \(M\) of a \([kd- 1, kd+ 1]\)-graph \(G\), there is a \([k- 1, k+ 1]\)-factorization of \(G\) orthogonal to \(M\) where \(k\geq 2\) is an integer.
scientific article; zbMATH DE number 906658