Spectral conditions of pancyclicity for t-tough graphs
<|reference_start|>Spectral conditions of pancyclicity for t-tough graphs: More than 40 years ago Chv\'atal introduced a new graph invariant, which he called graph toughness. From then on a lot of research has been conducted, mainly related to the relationship between toughness conditions and the existence of cyclic structures, in particular, determining whether the graph is Hamiltonian and pancyclic. A pancyclic graph is certainly Hamiltonian, but not conversely. Bondy in 1976, however, suggested the "metaconjecture" that almost any nontrivial condition on a graph which implies that the graph is Hamiltonian also implies that the graph is pancyclic. We confirm the Bondy conjecture for t-tough graphs in the case when $t\in \{ 1;2;3\}$ in terms of the edge number, the spectral radius and the signless Laplacian spectral radius of the graph.<|reference_end|>
@article{benediktovich2024spectral,
    title={Spectral conditions of pancyclicity for t-tough graphs},
    author={Vladimir I. Benediktovich},
    journal={arXiv preprint arXiv:2406.17089},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.17089},
    primaryClass={math.CO cs.DM}
}