Almost resolvable k ‐cycle systems with k ≡ 2 ( mod 4 )

In this paper, we show that if k ≥ 6 and k ≡ 2 ( mod 4 ) , then there exists an almost resolvable k ‐cycle system of order 2 k t + 1 for all t ≥ 1 except possibly for t = 2 and k ≥ 14 . Thus we give a partial solution to an open problem posed by Lindner, Meszka, and Rosa (J. Combin. Des., vol. 17, pp. 404–410, 2009).