The number of triangles in 2-factorizations of K2n minus a 1-factor - Meng, Xianchen; Zhang, Yan; Du, Beiliang (Utilitas Mathematica, 2013)
A 2-factorization of Kn is a partition of the edge set of K n into 2-factors. Given an arbitrary 2-factorization F = F 1,F2,... Fn-1 of K2n,let δi,be the number of triangles contained in Fi and let δ = Σδi. Then F is said to be a 2-factorization with δ triangles. Denote by Δ(2ra),the set of all δ such that there exists a 2-factorization with 6 triangles. Let (equation) where (equation). In this paper,we consider the problem of constructing 2-factorization of K2n containing a specified number of triangles. We proved that apart from some exceptions Δ(2n) = PΔ(2n).