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{\bf Makoto Araya and G\'abor Wiener }
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{\bf On Cubic Planar Hypohamiltonian and Hypotraceable Graphs}
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We present a cubic planar hypohamiltonian graph on 70 vertices,
improving the best known bound of 94 by Thomassen and derive some
consequences concerning longest paths and cycles of planar
$3$-connected graphs. We also show that cubic planar hypohamiltonian
graphs on $n$ vertices exist for every even number $n\geq 86$ and that
cubic planar hypotraceable graphs exist on $n$ vertices for every even
number $n \geq 356$, settling an open question of Holton and Sheehan.

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