Abstract
An n-vertex graph G is called Hamiltonian if it contains a cycle of length n. Denote by \(\delta (G)\) the minimum degree of G. The celebrated Dirac theorem states that every n-vertex graph with \(\delta (G)\ge n/2\) is Hamiltonian for \(n\ge 3\). In the present paper, we identify all 2-connected n-vertex non-Hamiltonian graphs with \(\delta (G)\ge \lfloor n/2\rfloor -1\) for \(n\ge 21\).
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Acknowledgements
The work was supported by the National Natural Science Foundation of China (No. 72004154). We would like to thank the referees for their valuable comments and suggestions.
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Communicated by Wen Chean Teh.
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Fu, L., Gao, L., Wang, J. et al. Non-Hamiltonian Graphs with Large Minimum Degree. Bull. Malays. Math. Sci. Soc. 47, 32 (2024). https://doi.org/10.1007/s40840-023-01615-x
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DOI: https://doi.org/10.1007/s40840-023-01615-x