# Alspach, Brian

## Hamilton decomposition of prisms over 3-connected cubic planar graphs ★★

\begin{conjecture} Every prism over a $3$-connected cubic planar graph can be decomposed into two Hamilton cycles. \end{conjecture}

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## Decomposing an even tournament in directed paths. ★★★

Author(s): Alspach; Mason; Pullman

\begin{conjecture} Every tournament $D$ on an even number of vertices can be decomposed into $\sum_{v\in V}\max\{0,d^+(v)-d^-(v)\}$ directed paths. \end{conjecture}

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