A planar hypotraceable graph is a hypotraceable graph that is also planar. A number of planar hypotraceable graphs are illustrated above.
Using a theorem of Thomassen (1974), the Wiener-Araya graph on 42 vertices can be used to construct a planar hypotraceable graph on 162 vertices, smaller than the 186-vertex graph obtained from the 48-Zamfirescu graph using Thomassen's construction. These graphs are implemented in the Wolfram Language as GraphData["PlanarHypohamiltonian", 162] and GraphData["PlanarHypohamiltonian", 186], respectively.
Jooyandeh et al. (2017) showed that there exist planar hypotraceable graphs on 154 vertices, as well as on all vertex counts greater than or equal to 156.
Using the 70-node Araya-Wiener graph, a 340-node cubic planar hypotraceable graph can be constructed (Araya and Wiener 2011).
Holton and Sheehan (1993) asked if there exists an integer such that a cubic planar hypotraceable graph exists for every even integer , and Araya and Wiener (2011) settled the question with .