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 .
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