Almost resolvable $k$-cycle systems with $k\equiv 2(\mathrm{mod}4)$

Abstract

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

cycle system; almost resolvable cycle system. arXiv admin note: substantial text overlap with arXiv:1706.05958, arXiv:1605.00818

References in corpus (1)

• Completing the spectrum of almost resolvable cycle systems with odd cycle length