Almost resolvable $k$-cycle systems with $k\equiv 2\pmod 4$

Abstract

In this paper, we show that if $k\geq 6$ and $k \equiv 2 \pmod 4$, then there exists an almost resolvable $k$-cycle system of order $2kt+1$ for all $t\ge 1$ except possibly for $t=2$ and $k\geq 14$. 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).