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Being Hamiltonian is not a Tutte invariant. (English) Zbl 0751.05067
Author’s abstract: T. Brylawski and J. Oxley asked, if the size of the largest circuit in a graph is a Tutte invariant. We show by an example, that this is not the case.

MSC:
05C45 Eulerian and Hamiltonian graphs
05C38 Paths and cycles
05C99 Graph theory
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References:
[1] Brylawski, T.H.; Oxley, J.G., The Tutte polynomial and its applications, () · Zbl 0769.05026
[2] Welsh, D.J.A., Matroid theory, (1976), Academic Press London · Zbl 0343.05002
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