# Jackson, Bill

## Hamilton cycle in small d-diregular graphs ★★

Author(s): Jackson

An directed graph is $k$-diregular if every vertex has indegree and outdegree at least $k$.

\begin{conjecture} For $d >2$, every $d$-diregular oriented graph on at most $4d+1$ vertices has a Hamilton cycle. \end{conjecture}

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## Long directed cycles in diregular digraphs ★★★

Author(s): Jackson

\begin{conjecture} Every strong oriented graph in which each vertex has indegree and outdegree at least $d$ contains a directed cycle of length at least $2d+1$. \end{conjecture}

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