High Quality Content by WIKIPEDIA articles! 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 4, 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 the 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.

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