Journal of the
Korean Mathematical Society JKMS

A digraph $T$ is called a local tournament if for every vertex $x$ of $T$, the set of in-neighbors as well as the set of out-neighbors of $x$ induce tournaments. Let $x$ and $y$ be two vertices of a 3-connected and arc-3-cyclic local tournament $T$ with $y\not\to x$. We investigate the structure of $T$ such that $T$ contains no $(x,y)$-path of length $k$ for some $k$ with $3\le k\le |V(T)|-1$. Our result generalizes those of \cite{arp} and \cite{gv8} for tournaments.

Keywords: bypath, cycle, strong connectivity, local tournament

MSC numbers: 05C20, 05C38