Journal of the
Korean Mathematical Society JKMS

A digraph is locally semicomplete if for every vertex $x$, the set of in-neighbors as well as the set of out-neighbors of $x$ induce semicomplete digraphs. Let $D$ be a $k$-connected locally semicomplete digraph with $k\ge 3$ and $\overline{g}$ denote the length of a longest induced cycle of $D$. It is shown that if $D$ has at least $7(k-1)\overline{g}$ vertices, then $D$ has a factor composed of $k$ cycles; furthermore, if $D$ is semicomplete and with at least $5k+1$ vertices, then $D$ has a factor composed of $k$ cycles and one of the cycles is of length at most 5. Our results generalize those of [3] for tournaments to locally semicomplete digraphs.

Keywords: cycle, factor, strong connectivity, locally semicomplete digraph

MSC numbers: 05C20, 05C38