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Thomassen Graphs

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ThomassenGraphs

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 60-vertex Thomassen graph has graph crossing number 12.

ThomassenGraph34

"The" Thomassen graph (Thomassen 1974a) is the hypotraceable graph on 34 vertices and 52 edges illustrated above in two embeddings.

ThomassenHypohamiltonian

A number of hypohamiltonian graphs appearing in Thomassen (1974b, 1981, 1974b, 1974b, 1981, 1976, respectively), are illustrated above.

ThomassenHypotraceable

A number of hypotraceable graphs appearing in Thomassen (1974a, 1976), respectively, are illustrated above.

See also

Hypohamiltonian Graph, Hypotraceable Graph, Planar Hypohamiltonian Graph

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References

Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, p. 240, 1976.House of Graphs. Thomassen Graphs. Thomassen Graph 20, Thomassen 24 non-planar cubic hypohamiltonian, Thomassen Graph 32, Thomassen Graph 34, Thomassen Graph 41, Thomassen Graph 60, Thomassen Graph 94, and Thomassen Graph 105.Thomassen, C. "Hypohamiltonian and Hypotraceable Graphs." Disc. Math. 9, 91-96, 1974a.Thomassen, C. "On Hypohamiltonian Graphs." Disc. Math. 10, 383-390, 1974b.Thomassen, C. "Planar and Infinite Hypohamiltonian and Hypotraceable Graphs." Disc. Math 14, 377-389, 1976.Thomassen, C. "Planar Cubic Hypohamiltonian and Hypotraceable Graphs." J. Comb. Th. B 30, 36-44, 1981.

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Thomassen Graphs

Cite this as:

Weisstein, Eric W. "Thomassen Graphs." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ThomassenGraphs.html

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