The Hamilton–Waterloo Problem with C16-Factors and Cm-Factors for Odd m

The Hamilton–Waterloo problem is a problem of graph factorization. The Hamilton–Waterloo problem HWP(H;m,n;α,β) asks for a two-factorization of a graph H containing α Cm-factors and β Cn-factors. Let Kv* denote the complete graph Kv if v is odd and Kv minus a one-factor if v is even. In this paper, we completely solve the Hamilton–Waterloo problem HWP(Kv*;m,16;α,β) for odd m≥9 and α≥15.