The name "Thomassen graph" is used for a number of hypotraceable and hypohamiltonian graphs associated with Carsten Thomassen. These graphs, illustrated above, are implemented in the Wolfram Language as GraphData["ThomassenGraphXXX"] for XXX equal to 20, 24, 32, 60, 94, and 105.
The 20- and 24-vertex Thomassen graphs have graph crossing number 6 and 4, respectively. The 32- and 34-vertex Thomassen graphs both have graph crossing number 8 (E. Weisstein, Oct. 5, 2026). The 41-vertex Thomassen graph has graph crossing number 9 (E. Weisstein, Sep. 24, 2026). The 60-vertex Thomassen graph has graph crossing number 12. The 94- and 105-vertex Thomassen graphs are planar.
"The" Thomassen graph (Thomassen 1974a) is the hypotraceable graph on 34 vertices and 52 edges illustrated above in two embeddings.
A number of hypohamiltonian graphs appearing in Thomassen (1974b, 1981, 1974b, 1974b, 1981, 1976, respectively), are illustrated above.
A number of hypotraceable graphs appearing in Thomassen (1974a, 1976), respectively, are illustrated above.
