Hamiltonian paths and cycles | Planar graphs | Regular graphs | Individual graphs

Tutte graph

In the mathematical field of graph theory, the Tutte graph is a 3-regular graph with 46 vertices and 69 edges named after W. T. Tutte. It has chromatic number 3, chromatic index 3, girth 4 and diameter 8. The Tutte graph is a cubic polyhedral graph, but is non-hamiltonian. Therefore, it is a counterexample to Tait's conjecture that every 3-regular polyhedron has a Hamiltonian cycle. Published by Tutte in 1946, it is the first counterexample constructed for this conjecture. Other counterexamples were found later, in many cases based on Grinberg's theorem. (Wikipedia).

Tutte graph
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Related pages

Graph theory | Regular graph | Chromatic number | Characteristic polynomial | Grinberg's theorem | Mathematics | Barnette–Bosák–Lederberg graph | Planar graph | Cubic graph | Cyclic group | W. T. Tutte | Polyhedral graph | Pentagonal prism | Tait's conjecture