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Independent dominating sets and Hamiltonian cycles. (English) Zbl 1112.05077
Summary: A graph is uniquely Hamiltonian if it contains exactly one Hamiltonian cycle. In this note we prove that there are no \(r\)-regular uniquely Hamiltonian graphs when \(r > 22\). This improves upon earlier results of C. Thomassen [J. Comb. Theory, Ser. B 72, 104–109 (1998; Zbl 0895.05038)].

MSC:
05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
05C45 Eulerian and Hamiltonian graphs
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