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arxiv: 1710.00647 · v3 · pith:MBK7OUB6new · submitted 2017-09-25 · 🧮 math.CO

Almost resolvable k-cycle systems with kequiv 2pmod 4

classification 🧮 math.CO
keywords almostcycleequivpmodresolvablecombinexceptexists
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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).

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