Abstract
Using a construction of Thomassen [Discrete Math. 9, 91–96 (1974)] we prove that for infinitely manyn there is a familyℱ n of triangle-free maximally non-hamiltonian graphs of ordern with |ℱ n | → ∞ exponentially inn. In particular, for everym ≧ 48 we construct such a graph; an infinite number of these provide new “almost extremal” examples in the sense of minimal size.
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References
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Thomassen, C.: Hypohamiltonian and hypotraceable graphs. Discrete Math.9, 91–96 (1974)
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Horák, P., Širáň, J. On a construction of Thomassen. Graphs and Combinatorics 2, 347–350 (1986). https://doi.org/10.1007/BF01788108
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DOI: https://doi.org/10.1007/BF01788108