Araya and Wiener (2011) found the two cubic planar hypohamiltonian graphs on 70 and 88 vertices, respectively, illustrated above.
Araya-Wiener Graphs
See also
Cubic Graph, Hypohamiltonian Graph, Planar Graph, Planar Hypohamiltonian Graph, Wiener-Araya GraphExplore with Wolfram|Alpha
References
Araya, M. and Wiener, G. "On Cubic Planar Hypohamiltonian and Hypotraceable Graphs." Elec. J. Combin. 18, 2011. https://www.combinatorics.org/ojs/index.php/eljc/article/view/v18i1p85/.House of Graphs. Araya-Wiener Graphs. Cubic planar hypohamiltonian Araya-Wiener graph on 70 vertices and Araya-Wiener Graph 88.Referenced on Wolfram|Alpha
Araya-Wiener GraphsCite this as:
Weisstein, Eric W. "Araya-Wiener Graphs." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Araya-WienerGraphs.html