Araya and Wiener (2011) found the two cubic planar hypohamiltonian Araya-Wiener graphs on 70 and 88 vertices. McKay and Jooyandeh subsequently found an additional 6 cubic planar hypohamiltonian graphs on 70 vertices (McKay), the first of which was independently rediscovered by Tsai (2024v1). It is known that no such graph exists on 42 or fewer vertices (Aldred et al. 2000, Araya and Wiener 2011). While the smallest possible number of vertices for a cubic planar hypohamiltonian graph is not known, it must lie between 54 and 70 vertices inclusive (Goedgebeur and Zamfirescu 2017, Tsai 2024).
Araya and Wiener (2011) showed that a cubic planar hypohamiltonian graph on 
vertices exists for every nonnegative even integer 
. Holton and Sheehan (1993) asked if there exists an integer
such that a cubic planar hypohamiltonian graph exists for every even integer 
,
and Araya and Wiener (2011) settled the question with 
.
