Near 2-factorizations of \(2K_ n:\) Cycles of even length
A near 2-factor in a graph G is a subgraph in which each vertex, except for one vertex of degree zero, has degree 2. A t-uniform near 2- factorization of \(2K_ m\) (two edges between every pair of distinct vertices) is a partition of \(E(2K_ m)\) into near 2-factors all of whose cycles have length t. The authors prove that \(2K_ m\) has a t-uniform near 2-factorization if and only if \(m\equiv l(mod t)\), whenever t is even. They also consider 4-uniform near 2-factorizations of \(2K_ m\) with the property that if one of the near 2-factors is known, all others can easily be generated from it. They find infinitely many m for which there are such 4-uniform near 2-factorizations.
t-uniform near 2-factorization of \(2K_ m\)
scientific article; zbMATH DE number 4204386